Lectures on Differential Equations and Differential Geometry 微分方程和微分几何（英文版）

样章

作者：

Louis Nirenberg （路易斯·尼伦伯格）

定价：

89.00 元

版面字数：

300千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2021年

ISBN：

978-7-04-050302-9

物料号：

50302-00

出版时间：

2018-09-25

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
- Front Matter
- Part I Existence Theorems in Partial Differential Equations
  - 1 Preliminaries.
    - 1.1 Introduction.
    - 1.2 TheMaximumPrinciple
    - 1.3 Consequences of theMaximumPrinciple
  - 2 The Potential Equation
    - 2.1 Fundamental Solution
    - 2.2 The Poisson Integral Formula
    - 2.3 TheMean Value Property of Potential Functions
    - 2.4 Estimates of Derivatives of Harmonic Functions and Analyticity
    - 2.5 The Theorems and Inequality ofHarnack
    - 2.6 Theoremon Removable Singularities
  - 3 The PerronMethod for Solving the Dirichlet Problem
    - 3.1 The PerronMethod
    - 3.2 The PerronMethod forMore General Elliptic Equations
  - 4 SchauderEstimates.
    - 4.1 Poisson’s Equation
    - 4.2 A Preliminary Estimate
    - 4.3 Statement of Schauder’s Estimates
    - 4.4 Some Applications of the Interior Estimates
    - 4.5 The BoundaryValue Problem
    - 4.6 Strong Barrier Functions, and the Boundary Value Problem
  - 5 Derivation of the Schauder Estimates
    - 5.1 A Preliminary Estimate
    - 5.2 A Further Investigation of the Poisson Equation
    - 5.3 Completion of the Interior Estimates
- Part II Seminar on Differential Geometry in the Large
  - 1 Complete Surfaces
  - 2 The Formof Complete Surfaces of Positive Gauss Curvature in Three-dimensional Space
    - 2.1 Hadamard’s Principle
    - 2.2 Completeness of a Surface
    - 2.3 Examples Showing that the Properties V , V _ and E are Independent
    - 2.4 Main Theorem.
    - 2.5 Consequence
    - 2.6 Analogous Theorems for Plane Curves
    - 2.7 Proof of Theorem2.1
  - 3 On Surfaces with Constant Negative Gauss Curvature
    - 3.1 Hilbert’s TheoremonHyperbolic Surfaces
    - 3.2 Asymptotic Coordinates in the Small
    - 3.3 Considerations in the Large.
    - 3.4 Bounds on the Extended Angle Function.
  - 4 Isometric Deformations in the Small
  - 5 Rigidity of Closed Convex Surfaces
  - 6 Rigid Open Convex Surfaces
  - 7 Rigidity of Sphere
  - 8 Uniqueness of Closed Convex Surfaces with Prescribed Line Element
  - 9 A Theoremof Christoffel on Closed Surfaces
  - 10 Minkowski’s Problem
  - 11 Existence of a Closed Convex Surface Solving Minkowski’s Problem
- About the author