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

版面字数：

160千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2021年

ISBN：

978-7-04-053499-3

物料号：

53499-00

出版时间：

2020-05-07

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

目录
- 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