Partial Differential Equations

This textbook is intended for students who wish to obtain an introduction to the theory of partial di?erential equations (PDEs, for short), in particular, those of elliptic type. Thus, it does not o?er a comprehensive overview of the whole ?eld of PDEs, but tries to lead the reader to the most impor...

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Main Author: Jost, Jürgen
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 2002, 2002
Edition:1st ed. 2002
Series:Graduate Texts in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Introduction: What Are Partial Differential Equations?
  • The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order
  • The Maximum Principle
  • Existence Techniques I: Methods Based on the Maximum Principle
  • Existence Techniques II: Parabolic Methods. The Heat Equation
  • The Wave Equation and Its Connections with the Laplace and Heat Equations
  • The Heat Equation, Semigroups, and Brownian Motion
  • The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)
  • Sobolev Spaces and L2 Regularity Theory
  • Strong Solutions
  • The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV)
  • The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash