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21. A course on partial differential equations [2018]
 Craig, Walter, 1953 author.
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — ix, 205 pages : illustrations ; 27 cm.
 Summary

 Introduction Wave equations The heat equation Laplace's equation Properties of the Fourier transform Wave equations on $\mathbb{R}^n$ Dispersion Conservation laws and shocks Bibliography Index.
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QA377 .C85 2018  Unknown 
 PSPDE (Conference) (5th : 2016 : Braga, Portugal)
 Cham : Springer, 2018.
 Description
 Book — 1 online resource (172 p.).
 Summary

 preliminary Benjamim Anwasia (CMAT, University of Minho)  Kinetic Theory & PDESs
 Christophe Bahadoran (Blaise Pascal University, France)  Interacting Particle Systems
 Giada Basile (Universita di Roma `La Sapienza', Italy)  Interacting Particle Systems
 Cedric Bernardin (University of Nice, France)  Interacting Particle Systems
 Marzia Bisi (University of Parma, Italy)  Kinetic Theory & Modelling
 Oriane Blondel (University Claude Bernard, Lyon 1, France)  Interacting Particle Systems
 Yann Brenier (Ecole Polytechnique, France)  Kinetic Theory & PDEs
 Jose A. Canizo (University of Granada, Spain)  Kinetic Theory & PDEs
 Eric Carlen (Rutgers University, USA)  Kinetic Theory & PDEs
 Jose Antonio Carrillo de la Plata (Imperial College London, UK)  Kinetic Theory & PDEs
 Filipe Carvalho (CMAT, University of Minho)  Kinetic Theory & Modelling
 M. Conceicao Carvalho (CMAF, University of Lisbon)  Kinetic Theory & PDEs
 Conrado da Costa (University of Leiden, Netherlands)  Interacting Particle Systems
 Francois Delarue (University of Nice, France)  Probability & PDEs
 Clement Erignoux (Ecole Polytechnique, France)  Interacting Particle Systems
 Francois Golse (Ecole Polytechnique, CMLS, France)  Kinetic Theory & PDEs
 Patricia Goncalves (CAMGSD, University of Lisbon)  Interacting Particle Systems
 Maria Groppi (University of Parma, Italy)  Kinetic Theory & Modelling
 Francois Huveneers (Paris Dauphine University, France)  Interacting Particle Systems
 Milton Jara (IMPA, Brazil)  Interacting Particle Systems
 Stefano Olla (Paris Dauphine University, France)  Interacting Particle Systems
 Byron Oviedo (University of Nice, France)  Interacting Particle Systems
 Nicolas Perkowski (HumboldtUniversitat zu Berlin)  Interacting Particle Systems
 Valeria Ricci (University of Palermo, Italy)  Kinetic Theory & PDEs
 Gunter Schutz (Institute of Complex Systems II, Germany)  Interacting Particle Systems
 Ana Jacinta Soares (CMAT, University of Minho)  Kinetic Theory & Modelling
 Cinzia Soresina (University of Milano, Italy)  Kinetic Theory & Modelling
 Rui Vilela Mendes (University of Lisbon, Portugal)  PDEs & Modelling
 Hendrik Weber (Warwick University, UK)  Interacting Particle Systems
 Bernt Wennberg (University of Gothenburg, Sweden)  Kinetic Theory & Modelling.
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 Kavallaris, Nikos I.
 Cham : Springer, [2018]
 Description
 Book — 1 online resource. Digital: text file; PDF.
 Summary

 Dedication. Preface. Acknowledgements. Part I Applications in Engineering. Microelectromechanicalsystems(MEMS). Ohmic Heating Phenomena. Linear Friction Welding. Resistance Spot Welding. Part II Applications in Biology. GiererMeinhardt System. A Nonlocal Model Illustrating Replicator Dynamics. A Nonlocal Model Arising in Chemotaxis. A Nonlocal ReactionDiffusion System Illustrating Cell Dynamics. Appendices. Index.
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 Figalli, Alessio, 1984 author.
 Cham, Switzerland : Springer, [2018]
 Description
 Book — ix, 214 pages : illustrations ; 24 cm.
 Summary

 Alberto Farina and Enrico Valdinoci:Introduction.Alessio Figalli:Global Existence for the SemiGeostrophic Equations via Sobolev Estimates for MongeAmpere.Ireneo Peral Alonso: On Some Elliptic and Parabolic Equations Related to Growth Models. Enrico Valdinoci: All Functions are (locally) Sharmonic (up to a small error)  and Applications.
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25. Analytical methods for kolmogorov equations [2017]
 Lorenzi, Luca, author.
 Second edition.  Boca Raton : CRC Press, [2017]
 Description
 Book — xl, 566 pages ; [ca. 2329] cm.
 Summary

 Markov semigroups in RN. Markov semigroups in unbounded open sets. A class of Markov semigroups in RN associated with degenerate elliptic operators. The nonautonomous setting. Appendices.
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 David, Guy, 1957 author.
 Paris : Société Mathématique de France, 2017.
 Description
 Book — ii, 203 pages ; 24 cm.
 Online
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Shelved by Series title V.392  Unknown 
 Salsa, S., author.
 Third edition.  Switzerland : Springer, [2016]
 Description
 Book — 1 online resource (xviii, 686 pages) : illustrations.
 Summary

 1 Introduction. 2 Diffusion. 3 The Laplace Equation. 4 Scalar Conservation Laws and First Order Equations. 5 Waves and vibrations. 6 Elements of Functional Analysis. 7 Distributions and Sobolev Spaces. 8 Variational formulation of elliptic problems. 9 Further Applications. 10 Weak Formulation of Evolution Problems. 11 Systems of Conservation Laws. 12 A Fourier Series. 13 B Measures and Integrals. 14 C Identities and Formulas.
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 Schönlieb, CarolaBibiane, author.
 Cambridge : Cambridge University Press, 2015.
 Description
 Book — 1 online resource : digital, PDF file(s).
 Summary

 1. Introduction
 2. Overview of mathematical inpainting methods
 3. The principle of good continuation
 4. Secondorder diffusion equations for inpainting
 5. Higherorder PDE inpainting
 6. Transport inpainting
 7. The MumfordShah image for inpainting
 8. Inpainting mechanisms of transport and diffusion
 9. Applications.
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 Vasy, András, author.
 Providence, Rhode Island : American Mathematical Society, [2015]
 Description
 Book — x, 281 pages : illustrations ; 27 cm.
 Summary

 * Introduction* Where do PDE come from* First order scalar semilinear equations* First order scalar quasilinear equations* Distributions and weak derivatives* Second order constant coefficient PDE: Types and d'Alembert's solution of the wave equation* Properties of solutions of second order PDE: Propagation, energy estimates and the maximum principle* The Fourier transform: Basic properties, the inversion formula and the heat equation* The Fourier transform: Tempered distributions, the wave equation and Laplace's equation* PDE and boundaries* Duhamel's principle* Separation of variables* Inner product spaces, symmetric operators, orthogonality* Convergence of the Fourier series and the Poisson formula on disks* Bessel functions* The method of stationary phase* Solvability via duality* Variational problems* Bibliography* Index.
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QA377 .V38 2015  Unknown 
 Shearer, Michael, author.
 Princeton : Princeton University Press, [2015]
 Description
 Book — x, 274 pages : illustrations ; 26 cm
 Summary

This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors.
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QA374 .S45 2015  Unknown 
 Rădulescu, Vicenţiu D., 1958 author.
 Boca Raton, FL : CRC Press, [2015]
 Description
 Book — xxi, 301 pages : illustrations ; 24 cm.
 Summary

 Isotropic and Anisotropic Function Spaces Lebesgue and Sobolev Spaces with Variable Exponent History of function spaces with variable exponent Lebesgue spaces with variable exponent Sobolev spaces with variable exponent Dirichlet energies and EulerLagrange equations Lavrentiev phenomenon Anisotropic function spaces Orlicz spaces
 Variational Analysis of Problems with Variable Exponents Nonlinear Degenerate Problems in NonNewtonian Fluids Physical motivation A boundary value problem with nonhomogeneous differential operator Nonlinear eigenvalue problems with two variable exponents A sublinear perturbation of the eigenvalue problem associated to the Laplace operator Variable exponents versus Morse theory and local linking The CaffarelliKohnNirenberg inequality with variable exponent
 Spectral Theory for Differential Operators with Variable Exponent Continuous spectrum for differential operators with two variable exponents A nonlinear eigenvalue problem with three variable exponents and lack of compactness Concentration phenomena: the case of several variable exponents and indefinite potential Anisotropic problems with lack of compactness and nonlinear boundary condition
 Nonlinear Problems in OrliczSobolev Spaces Existence and multiplicity of solutions A continuous spectrum for nonhomogeneous operators Nonlinear eigenvalue problems with indefinite potential Multiple solutions in OrliczSobolev spaces Neumann problems in OrliczSobolev spaces
 Anisotropic Problems: Continuous and Discrete Anisotropic Problems Eigenvalue problems for anisotropic elliptic equations Combined effects in anisotropic elliptic equations Anisotropic problems with noflux boundary condition Bifurcation for a singular problem modelling the equilibrium of anisotropic continuous media
 Difference Equations with Variable Exponent Eigenvalue problems associated to anisotropic difference operators Homoclinic solutions of difference equations with variable exponents Lowenergy solutions for discrete anisotropic equations
 Appendix A: Ekeland Variational Principle Appendix B: Mountain Pass Theorem Bibliography Index A Glossary is included at the end of each chapter.
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QA377 .R33 2015  Unknown 
32. Applied partial differential equations [2015]
 Logan, J. David (John David), author.
 Third edition.  New York : Springer, [2014]
 Description
 Book — 1 online resource (x, 289 pages) : illustrations.
 Summary

 Intro; Contents; Preface to the Third Edition; To Students; 1 The Physical Origins of Partial Differential Equations; 1.1 PDE Models; 1.2 Conservation Laws; 1.3 Diffusion; 1.4 Diffusion and Randomness; 1.5 Vibrations and Acoustics; 1.6 Quantum Mechanics*; 1.7 Heat Conduction in Higher Dimensions; 1.8 Laplace's Equation; 1.9 Classification of PDEs; 2 Partial Differential Equations on Unbounded Domains; 2.1 Cauchy Problem for the Heat Equation; 2.2 Cauchy Problem for the Wave Equation; 2.3 WellPosed Problems; 2.4 SemiInfinite Domains; 2.5 Sources and Duhamel's Principle
 2.6 Laplace Transforms2.7 Fourier Transforms; 3 Orthogonal Expansions; 3.1 The Fourier Method; 3.2 Orthogonal Expansions; 3.3 Classical Fourier Series; 4 Partial Differential Equations on Bounded Domains; 4.1 Overview of Separation of Variables; 4.2 SturmLiouville Problems; 4.3 Generalization and Singular Problems; 4.4 Laplace's Equation; 4.5 Cooling of a Sphere; 4.6 Diffusion in a Disk; 4.7 Sources on Bounded Domains; 4.8 Poisson's Equation*; 5 Applications in the Life Sciences; 5.1 AgeStructured Models; 5.2 Traveling Waves Fronts; 5.3 Equilibria and Stability
 6 Numerical Computation of Solutions6.1 Finite Difference Approximations; 6.2 Explicit Scheme for the Heat Equation; 6.3 Laplace's Equation; 6.4 Implicit Scheme for the Heat Equation; A Differential Equations; References; Index
33. Elements of partial differential equations [2014]
 Drábek, Pavel, 1953 author.
 2nd, revised and extended edition.  Berlin ; Boston : De Gruyter, [2014]
 Description
 Book — xiii, 277 pages : illustrations ; 25 cm.
 Summary

This textbook is an elementary introduction to the basic principles of partial differential equations. With many illustrationsitintroduces PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. The book is addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics.
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QA374 .D66 2014  Unknown 
34. Formal algorithmic elimination for PDEs [2014]
 Robertz, Daniel, 1977 author.
 Cham : Springer, [2014]
 Description
 Book — viii, 283 pages : illustrations ; 24 cm.
 Summary

 Introduction. Formal Methods for PDE Systems. Differential Elimination for Analytic Functions. Basic Principles and Supplementary Material. References. List of Algorithms. List of Examples. Index of Notation. Index.
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Shelved by Series title V.2121  Unknown 
35. Introduction to partial differential equations for scientists and engineers using Mathematica [2014]
 Adzievski, Kuzman, author.
 Boca Raton, FL : CRC Press, [2014]
 Description
 Book — xiii, 634 pages : illustrations ; 25 cm
 Summary

 Fourier Series The Fourier Series of a Periodic Function Convergence of Fourier Series Integration and Differentiation of Fourier Series Fourier Sine and Fourier Cosine Series Mathematica Projects Integral Transforms The Fourier Transform and Elementary Properties Inversion Formula of the Fourier Transform Convolution Property of the Fourier Transform The Laplace Transform and Elementary Properties Differentiation and Integration of the Laplace Transform Heaviside and Dirac Delta Functions Convolution Property of the Laplace Transform Solution of Differential Equations by the Integral Transforms The SturmLiouville Problems Regular SturmLiouville Problem Eigenvalues and Eigenfunctions Eigenfunction Expansion Singular SturmLiouville Problem: Legendre's Equation Singular SturmLiouville Problem: Bessel's Equation Partial Differential Equations Basic Concepts and Definitions Formulation of Initial and Boundary Problems Classification of Partial Differential Equations Some Important Classical Linear Partial Differential Equations The Principle of Superposition First Order Partial Differential Equations Linear Equations with Constant Coefficients Linear Equations with Variable Coefficients First Order NonLinear Equations Cauchy's Method of Characteristics Mathematica Projects Hyperbolic Partial Differential Equations The Vibrating String and Derivation of the Wave Equation Separation of Variables for the Homogeneous Wave Equation D'Alambert's Solution of the Wave Equation Inhomogeneous Wave Equations Solution of the Wave Equation by Integral Transforms Two Dimensional Wave Equation: Vibrating Membrane The Wave Equation in Polar and Spherical Coordinates Numerical Solutions of the Wave Equation Mathematica Projects Parabolic Partial Differential Equations Heat Flow and Derivation of the Heat Equation Separation of Variables for the One Dimensional Heat Equation Inhomogeneous Heat Equations Solution of the Heat Equation by Integral Transforms Two Dimensional Heat Equation The Heat Equation in Polar and Spherical Coordinates Numerical Solutions of the Heat Equation Mathematica Projects Elliptic Partial Differential Equations The Laplace and Poisson Equations Separation of Variables for the Laplace Equation The Laplace Equation in Polar and Spherical Coordinates Poisson Integral Formula Numerical Solutions of the Laplace Equation Mathematica Projects Appendix A. Special Functions Appendix B. Table of the Fourier Transform of Some Functions Appendix C. Table of the Laplace Transform of Some Functions.
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QA377 .A47 2014  Unknown 
 Davis, John M.
 New York : W. H. Freeman & Co., c2013.
 Description
 Book — xii, 313 p., [4] p. of plates : ill. (some col.) ; 24 cm
 Summary

 Introduction to PDEs
 Fourier's method: separation of variables
 Fourier series theory
 General orthogonal series expansions
 PDEs in higher dimensions
 PDEs in other coordinate systems
 PDEs on unbounded domains
 Appendix.
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QA374 .D364 2013  Unknown 
37. Partial differential equations [2013]
 Jost, Jürgen, 1956
 Third edition.  New York : Springer, c2013.
 Description
 Book — xiii, 410 pages ; 24 cm.
 Summary

 Preface. Introduction: What are Partial Differential Equations?. 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order. 2 The Maximum Principle. 3 Existence Techniques I: Methods Based on the Maximum Principle. 4 Existence Techniques II: Parabolic Methods. The Heat Equation. 5 ReactionDiffusion Equations and Systems. 6 Hyperbolic Equations. 7 The Heat Equation, Semigroups, and Brownian Motion. 8 Relationships between Different Partial Differential Equations. 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III). 10 Sobolev Spaces and L^2 Regularity theory. 11 Strong solutions. 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV). 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash. Appendix: Banach and Hilbert spaces. The L^pSpaces. References. Index of Notation. Index.
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QA377 .J66 2013  Unknown 
 Basel : Birkhäuser, ©2011.
 Description
 Book — 1 online resource (vi, 367 pages).
 Summary

 Toeplitz operators and asymptotic equivariant index / L. Boutet de Monvel
 Boundary value problems of analytic and harmonic functions in a domain with piecewise smooth boundary in the frame of variable exponent Lebesgue spaces / V. Kokilashvili
 Edgedegenerate operators at conical exits to infinity / B.W. Schulze
 On a method for solving boundary problems for a thirdorder equation with multiple characteristics / Y.P. Apakov
 On stability and trace regularity of solutions to ReissnerMindlinTimoshenko equations / G. Avalos and D. Toundykov
 Linearization of a coupled system of nonlinear elasticity and viscous fluid / L. Bociu and J.P. Zolésio
 Some results of the identification of memory kernels / F. Colombo and D. Guidetti
 A kuniform maximum principle when 0 is an eigenvalue / G. Fragnelli and D. Mugnai
 Steadystate solutions for a general brusselator system / M. Ghergu
 Ordinary differential equations with distributions as coefficients in the sense of the theory of new generalized functions / U.U. Hrusheuski
 A boundary condition and spectral problems for the Newton potential / T. Sh. Kalmenov and D. Suragan
 An extremum principle for a class of hyperbolic type equations and for operators connected with them / I.U. Khaydarov, M.S. Salakhitdinov and A.K. Urinov
 Numerical investigations of tangled flows in a channel of constant and variable section at presence of recirculation zone / S. Khodjiev
 The optimal interior regularity for the critical case of a clamped thermoelastic system with point control revisited / C. Lebiedzik and R. Triggiani
 Multidimensional controllability problems with memory / P. Loreti and D. Sforza
 The Schrödinger flow in a compact manifold: highfrequency dynamics and dispersion / F. Macià
 Optimality of the asymptotic behavior of the energy for wave models / M. Reissig
 On singular systems of parabolic functional equations / L. Simon
 Boundaryvalue problems for a class of thirdorder composite type equations / O.S. Zikirov
 Shapemorphic metric, geodesic stability / J.P. Zolésio.
 Basel : Birkhäuser, c2011
 Description
 Book — vi, 367 p. : ill. ; 24 cm.
 Summary

 Toeplitz operators and asymptotic equivariant index / L. Boutet de Monvel
 Boundary value problems of analytic and harmonic functions in a domain with piecewise smooth boundary in the frame of variable exponent Lebesgue spaces / V. Kokilashvili
 Edgedegenerate operators at conical exits to infinity / B.W. Schulze
 On a method for solving boundary problems for a thirdorder equation with multiple characteristics / Y.P. Apakov
 On stability and trace regularity of solutions to ReissnerMindlinTimoshenko equations / G. Avalos and D. Toundykov
 Linearization of a coupled system of nonlinear elasticity and viscous fluid / L. Bociu and J.P. Zolésio
 Some results of the identification of memory kernels / F. Colombo and D. Guidetti
 A kuniform maximum principle when 0 is an eigenvalue / G. Fragnelli and D. Mugnai
 Steadystate solutions for a general brusselator system / M. Ghergu
 Ordinary differential equations with distributions as coefficients in the sense of the theory of new generalized functions / U.U. Hrusheuski
 A boundary condition and spectral problems for the Newton potential / T.Sh. Kalmenov and D. Suragan
 An extremum principle for a class of hyperbolic type equations and for operators connected with them / I.U. Khaydarov, M.S. Salakhitdinov and A.K. Urinov
 Numerical investigations of tangled flows in a channel of constant and variable section at presence of recirculation zone / S. Khodjiev
 The optimal interior regularity for the critical case of a clamped thermoelastic system with point control revisited / C. Lebiedzik and R. Triggiani
 Multidimensional controllability problems with memory / P. Loreti and D. Sforza
 The Schrödinger flow in a compact manifold: highfrequency dynamics and dispersion / F. Macià
 Optimality of the asymptotic behavior of the energy for wave models / M. Reissig
 On singular systems of parabolic functional equations / L. Simon
 Boundaryvalue problems for a class of thirdorder composite type equations / O.S. Zikirov
 Shapemorphic metric, geodesic stability / J.P. Zolésio.
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QA374 .M76 2011  Unknown 
40. Partial differential equations [2011  ]
 Taylor, Michael E., 1946
 2nd ed.  New York : Springer, c2011
 Description
 Book — v. : ill. ; 24 cm.
 Summary

 1. Basic theory
 2. Qualitative studies of linear equations
 3. Nonlinear equations.
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The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
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The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of CalderonZygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis.
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 Vol. 1: SpringerLink
 Vol. 2: SpringerLink
 Vol. 3: SpringerLink
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