- 相关
- 目录
- 笔记
- 书签
- Preface
- Contents
- 1 A Brief Review of Real and Functional Analysis
- 1.1 A Little Topological Uniqueness Trick
- 1.2 Integration Theory and the Lebesgue Convergence Theorems
- 1.3 Convolution and Mollification
- 1.4 Distribution Theory
- 1.5 Hölder and Sobolev Spaces
- 1.6 Duality and Weak Convergences in Sobolev Spaces
- 1.7 The Weak and Weak-Star Topologies
- 1.8 Variational Formulations and Their Interpretation
- 1.9 Some Spectral Theory
- Appendix: The Topologies of D and D'
- 2 Fixed Point Theorems and Applications
- 3 Superposition Operators
- 4 The Galerkin Method
- 5 The Maximum Principle, Elliptic Regularity, and Applications
- 6 Calculus of Variations and Quasilinear Problems
- 6.1 Lower Semicontinuity and Convexity
- 6.2 Application to Scalar Quasilinear Elliptic BoundaryValue Problems
- 6.3 Calculus of Variations in the Vectorial Case, Quasiconvexity
- 6.4 Quasiconvexity: A Necessary Condition and a SufficientCondition
- 6.5 Exercises of Chap.6
- Appendix: Weak Lower Semicontinuity Proofs
- 7 Calculus of Variations and Critical Points
- 8 Monotone Operators and Variational Inequalities
- References
- Index
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Nonlinear Elliptic Partial Differential Equations An Introduction
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