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半线性退化椭圆微分方程——局部定理与整体定理

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作者(越)阮明智

出版社哈尔滨工业大学出版社

ISBN9787560395142

出版时间2021-07

装帧平装

开本32开

定价48元

货号1202561193

上书时间2024-10-14

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INTRODUCTION

PART 1.INFINITE SMOOTHNESS OF SOLUTIONS

CHAPTER 1.FUNDAMENTAL SOLUTIONS AND NONBOUNDED SOLUTIONS OF LINEAR HOMOGENEOUS DEGENERATE ELLIPTIC EQUATIONS

1.1.Basic definitions,hypergeometric functions

1.2.The case of finite degeneracy

1.3.The case of infinite degeneracy

CHAPTER 2.SMOOTHNESS OF SOLUTIONS OF SEMILINEAR DEGENERATE ELLIPTIC EQUATIONS

2.1.Auxiliary results

2.2.Semilinear equations of HSrmanders type

2.3.Higher order semilinear hypoelliptic equations

2.4.Semilinear hypoelliptic equations of the Gilioli-Treves type

2.5.Equations with infinite degeneracy

PART 2.ANALYTICITY OF SOLUTIONS

CHAPTER 3.A NEW APPROACH FOR PROVING GEVREY REGULARITY OF SOLUTIONS OF ELLIPTIC EQUATIONS

3.1.Friedmans Lemmas

3.2.Weighted Holder spaces

3.3.Douglis-Nirenberg estimates

3.4.New argument in the proof of analyticity and Gevrey regularity of solutions

CHAPTER 4.ANALYTICITY AND GEVREY REGULARITY OF SOLUTIONS OF SEMILINEAR EQUATIONS OF MIZOHATA TYPE

4.1.Uniform fundamental solutions and representation formula

4.2.Infinite smoothness of solutions

4.3.Analyticity and Gevrey regularity of solutions

CHAPTER 5.ANALYTICITY AND GEVREY REGULARITY OF SOLUTIONS OF SEMILINEAR EQUATIONS OF THE GILIOLI-TREVES TYPE

5.1.A Model of Grushins type equations

5.2.Equation of tile Gilioli-Treves type

CHAPTER 6.ANALYTICITY AND GEVREY REGULARITY OF SOLUTIONS OF SEMILINEAR KOHN-LAPLACIAN ON THE HEISENBERG GROUP

6.1.Semilinear Kohn-Laplacian.

6.2.Fundamental solution of the Kohn-Laplacian

6.3.Oevrey regularityof solutions

PART 3.GLOBAL PROPERTIES OF SOLUTIONS

CHAPTER 7.EXISTENCE OF NONTRIVIAL SOLUTIONS TO BOUNDARY VALUE PROBLEMS FOR SEMILINEAR DEGENERATE ELLIPTIC EQUATIONS

7.1.Embedding theorems of Sobolevs type

7.2.Theorems on existence of solutions

CHAPTER 8.NON EXISTENCE OF NONTRIVIAL SOLUTIONS TO BOUNDARY VALUE PROBLEMS AND REGULARITY UP TO THE BOUNDARY

8.1 Generalized Pohozaevs identity and theorems on nonexistence of solutions

8.2.Regularity of solutions to boundary value problems up to the boundary

BIBLIOGRAPHY

LIST OF NOTATIONS AND ABBREVIATIONS

编辑手记

内容摘要
非线性椭圆型方程和线性退化椭圆型方程的边值问题及其解的光滑性已有一个多世纪的研究历史。本书基于作者对半线性退化椭圆微分方程的研究，即以线性和退化椭圆为主体的非线性方程展开论述。本书共分3部分，8章内容。