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Partial Differential Equations

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Author(s): Jürgen Jost (auth.)
Series: Graduate Texts in Mathematics 214
Edition: 1
Publisher: Springer New York
Year: 2002

Language: English
Pages: 338
Tags: Partial Differential Equations; Mathematical and Computational Physics; Numerical and Computational Methods

Introduction: What Are Partial Differential Equations?....Pages 1-6
The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order....Pages 7-30
The Maximum Principle....Pages 31-50
Existence Techniques I: Methods Based on the Maximum Principle....Pages 51-75
Existence Techniques II: Parabolic Methods. The Heat Equation....Pages 77-112
The Wave Equation and Its Connections with the Laplace and Heat Equations....Pages 113-125
The Heat Equation, Semigroups, and Brownian Motion....Pages 127-156
The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)....Pages 157-192
Sobolev Spaces and L 2 Regularity Theory....Pages 193-242
Strong Solutions....Pages 243-254
The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV)....Pages 255-274
The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash....Pages 275-307