微分方程和微分几何
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作者[加]路易斯·尼伦伯格（LouisNirenberg）,季理
出版社高等教育出版社
ISBN9787040503029
出版时间2018-09
版次1
装帧平装
开本16开
纸张胶版纸
页数174页
定价89元
上书时间2024-03-27
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基本信息
书名:微分方程和微分几何
定价：89.00元
作者:[加]路易斯·尼伦伯格（LouisNirenberg）,季理真
出版社：高等教育出版社
出版日期：2018-09-01
ISBN：9787040503029
字数：
页码：174
版次：
装帧：平装
开本：16开
商品重量：
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内容提要
There are long books and short books. It is hard to say which kind is more valuable， or which kind one should read. When a short book contains all essential things of a subject and arranges them in a clear and accessible way， a short book is probably more preferable for some obvious reasons. Additionally， ifit is written by aleading expert on the subjects and a master expositor， then the answer is a definite and clear yes. The booklet "Estence Theorems in Partial Differential Equations" is of this type. It was written by the world top expert on partial differential equations， Louis Nirenberg， at one of the peaks of his long and productive life. It covers estence and uniqueness of solutions of elliptic differential equations. When one opens thiooklet or rather lecture notes， one can immediately see the flow ofthoughts ofa great mathematician：it is direct to the point， everything moves smoothly and quickly， and there is no unnecessary discussions or digressions. Elliptic differential equations are central in partial differential equations and their applications in differential geometry. Though many results have been obtained in the past half century， the essential things are still the same. Furthermore， though there have been many books on differential equations， the freshness and the spirit of these lecture notes cannot be surpassed by later more comprehensive ones.
目录
Part I Estence Theorems in Partial Differential Equations1 Prelinunaries1．1 Introduction1．2 The Mamum Principle1．3 Consequences of the Mamum Principle2 The Potential Equation2．1 Fundamental Solution2．2 The Poisson Integral Formula2．3 The Mean Value Property of Potential Functions2．4 Estimates of Derivatives of Harmonic Functions and Analyticity2．5 The Theorems and Inequality of Harnack2．6 Theorem on Removable Singularities3 The Perron Method for Solving the Dirichlet Problem3．1 The Perron Method3．2 The Perron Method for More General Elliptic Equations4 Schauder Estimates4．1 Poisson's Equation4．2 A Preliminary Estimate4．3 Statement of Schauder's Estimates4．4 Some Applications of the Interior Estimates4．5 The Boundary Value Problem4．6 Strong Barrier Functions， and the Boundary Value Problem5 Derivation of the Schauder Estimates5．1 A Preliminary Estimate5．2 A Furtherlnvestigation of the Poisson Equation5．3 Completion of the Interior Estimates……Part II Seminar on Differential Geometry in the Large
作者介绍
序言
Part I Existence Theorems in Partial Differential Equations1 Prelinunaries1．1 Introduction1．2 The Maximum Principle1．3 Consequences of the Maximum Principle2 The Potential Equation2．1 Fundamental Solution2．2 The Poisson Integral Formula2．3 The Mean Value Property of Potential Functions2．4 Estimates of Derivatives of Harmonic Functions and Analyticity2．5 The Theorems and Inequality of Harnack2．6 Theorem on Removable Singularities3 The Perron Method for Solving the Dirichlet Problem3．1 The Perron Method3．2 The Perron Method for More General Elliptic Equations4 Schauder Estimates4．1 Poisson's Equation4．2 A Preliminary Estimate4．3 Statement of Schauder's Estimates4．4 Some Applications of the Interior Estimates4．5 The Boundary Value Problem4．6 Strong Barrier Functions， and the Boundary Value Problem5 Derivation of the Schauder Estimates5．1 A Preliminary Estimate5．2 A Furtherlnvestigation of the Poisson Equation5．3 Completion of the Interior Estimates……Part II Seminar on Differential Geometry in the Large
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