Partial Differential Equations

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This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Jost, Jürgen (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: New York, NY : Springer New York : Imprint: Springer, 2007.
Édition:2nd ed. 2007.
Collection:Graduate Texts in Mathematics, 214
Sujets:
Mathematical analysis.
Mathematical physics.
Differential equations.
Analysis.
Theoretical, Mathematical and Computational Physics.
Differential Equations.
Accès en ligne:Texto Completo
Table des matières:
  • 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.

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