非线性偏微分方程的弱收敛方法(影印版)
作者: Lawrence C.Evans
出版时间:2020-04
出版社:高等教育出版社
- 高等教育出版社
- 9787040534993
- 1版
- 296689
- 46254249-9
- 精装
- 16开
- 2020-04
- 160
- 100
- 理学
- 数学
- 数学类
- 研究生及以上
前辅文
Preface
Introduction
1. Weak Convergence
A. Review of Basic Theory
B. Convergence of Averages
C. Compactness in Sobolev Spaces
1. Embeddings
2. Compactness Theorems
3. Á Refinement of Rellich's Theorem
D. Measures of Concentration
1. Generalities
2. Defect Measures
3. Á Refinement of Fatou's Lemma
4. Concentration and Sobolev Inequalities
E. Measures of Oscillation
1. Generalities
2. Slicing Measures
3. Young Measures
2. Convexity
A. The Calculus of Variations
B. Weak Lower Semicontinuity
C. Convergence of Energies and Strong Convergence
3. Quasiconvexity
A. Definitions
1. Rank-One Convexity
2. Quasiconvexity
B. Weak Lower Semicontinuity
C. Convergence of Energies and Strong Convergence
D. Partial Regularity of Minimizers
E. Examples
1. Weak Continuity of Determinants
2. Polyconvexity
4. Concentrated Compactness
A. Variational Problems
1. Minimizers for Critical Sobolev Nonlinearities
2. Strong Convergence of Minimizing Sequences
B. Concentration-Cancellation
1. Critical Gradient Growth
2. Vorticity Bounds and Euler's Equations
5. Compensated Compactness
A. Direct Methods
1. Harmonie Maps into Spheres
2. Homogenization of Divergence Structure PDE'
3. Monotonicity, Minty-Browder Method in L
B. Div-Curl Lemma
C. Elliptic Systems
D. Conservation Laws
1. Single Equations
2. Systems of Two Equations
E. Generalization of Div-Curl Lemma
6. Maximum Principle Methods
A. The Maximum Principle for Fully Nonlinear PDE
1. Minty-Browder Method in L°°
2. Viscosity Solutions
B. Homogenization of Nondivergence Structure PDE's
C. Singular Perturbations
Appendix
Notes
References