非线性偏微分方程的弱收敛方法（影印版）

样章

作者：

Lawrence C. Evans

定价：

67.00元

ISBN：

978-7-04-053499-3

版面字数：

160.000千字

开本：

16开

全书页数：

暂无

装帧形式：

精装

重点项目：

暂无

出版时间：

2020-05-07

物料号：

53499-00

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

偏微分方程

暂无

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