Partial differential equations
 Responsibility
 Jürgen Jost.
 Language
 English.
 Edition
 Third edition.
 Imprint
 New York : Springer, c2013.
 Physical description
 xiii, 410 pages ; 24 cm.
 Series
 Graduate texts in mathematics ; 214.
Access
Available online
 dx.doi.org SpringerLink
Math & Statistics Library

Stacks

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QA377 .J66 2013

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QA377 .J66 2013
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Creators/Contributors
 Author/Creator
 Jost, Jürgen, 1956
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 This book offers an ideal graduatelevel introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including firstorder hyperbolic systems, Langevin and FokkerPlanck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Series
 Graduate texts in mathematics, 00725285 ; 214
 Available in another form
 Reproduction of (manifestation): Jost, Jürgen, 1956 Partial differential equations. New York : Springer, c2013 1 online resource (OCoLC)821020902
 ISBN
 9781461448082
 1461448085