Partial differential equations / Jurgen Jost.
By: Jost, Jurgen.
Material type: TextSeries: Graduate texts in mathematics ; 214.Publisher: New York : Springer, 2013Edition: 3rd ed.Description: xiii, 410 p. : ill. ; 24 cm.ISBN: 9781461448082.Subject(s): Partial differential equationsDDC classification: 515.353Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

Books 
ISI Library, Kolkata

515.353 J84 (Browse shelf)  Available  135856 
Includes bibliographical references and index.
1. Introduction: What Are Partial Differential Equations? 
2. The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order 
3. The Maximum Principle 
4. Existence Techniques I: Methods Based on the Maximum Principle 
5. Existence Techniques II: Parabolic Methods. The Heat Equation 
6. ReactionDiffusion Equations and Systems 
7. Hyperbolic Equations 
8. The Heat Equation, Semigroups, and Brownian Motion 
9. Relationships Between Different Partial Differential Equations 
10. The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III) 
11. Sobolev Spaces and L2 Regularity Theory 
12. Strong Solutions 
13. The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) 
14. The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash
Appendix
References
Index of notation
Index.
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.
There are no comments for this item.