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Partial Differential Equations Book

Partial Differential Equations
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Partial Differential Equations, 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 pr, Partial Differential Equations
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  • Partial Differential Equations
  • Written by author Jurgen Jost
  • Published by Springer-Verlag New York, LLC, 11/13/2012
  • 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 pr
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Preface
Introduction: What Are Partial Differential Equations? 1
1 The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order 7
2 The Maximum Principle 31
3 Existence Techniques I: Methods Based on the Maximum Principle 51
4 Existence Techniques II: Parabolic Methods. The Heat Equation 77
5 The Wave Equation and Its Connections with the Laplace and Heat Equations 113
6 The Heat Equation, Semigroups, and Brownian Motion 127
7 The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III) 157
8 Sobolev Spaces and L[superscript 2] Regularity Theory 193
9 Strong Solutions 243
10 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV) 255
11 The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash 275
App Banach and Hilbert Spaces. The L[superscript P]-Spaces 309
References 317
Index of Notation 319
Index 323


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Partial Differential Equations, 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 pr, Partial Differential Equations

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Partial Differential Equations, 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 pr, Partial Differential Equations

Partial Differential Equations

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Partial Differential Equations, 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 pr, Partial Differential Equations

Partial Differential Equations

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