Partial Differential Equations

There is also new material on Neumann boundary value problems, Poincaré inequalities, expansions, as well as a new proof of the Hölder regularity of solutions of the Poisson equation. Jürgen Jost is Co-Director of the Max Planck Institute for Mathematics in the Sciences and Professor of Mathematics...

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Main Author: Jost, Jürgen
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 2007, 2007
Edition:2nd ed. 2007
Series:Graduate Texts in Mathematics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - 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
  • Reaction-Diffusion Equations and Systems
  • 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