《二阶椭圆偏微分方程久应》是2003年世界图书市接用局衡罗可还直出版公司出版的图书。
出版社: 世界图书出版公司; 第1版 (2003年4月1日)
平装: 5172003受场41页
开本: 24开
ISBN: 7506259222
条形码: 9787506259224
尺寸: 22.2 x 14.8 x 来自2.6 cm
重量: 662 g
This revision of the 1983 second edition of"Elliptic Partial Differ360百科ential Equations of Second Order" corresponds to the Russian edition, published in 1989, in which we essentially updated the previous version to 1984. The ad动晶业讲对训ditional text relates to the boundary H61der derivative estimates of Nikolai Krylov, which provided a fundamental component of the fur拉部务细维职呢便争ther developm逐你名操林验ent of the classical theo触全类德越拿行最ry of elliptic (and parabolic), fully nonli损near equations in higher dim殖得亲袁河失ensions. In our presentation we adapted a simplification of Krylov's approach due to Luis Caffarelli.
Chapter 必素压上企1. Introduction
Part Ⅰ Linear Equ担怀居教ations
Chapter 2 Laplace's Equation
2.1 The M来自ean Value Ine口放殖地氢治象服站qualities
2.2 Maximum and Minimum Principle
2.3 The Harnack Inequality
2.4 Green's Representation
2.5 The Poisson Integral
2.6 Convergence Theorems
2.7 Interior Estimates of Derivatives
2.8 Th360百科e Dirichlet Problem; the Met给以伯体缺权势晶状侵hod of Subharmonic Functions
2.9 Capac认何高会掌烧某亮所ity
Problems
Chapter 3 The Clas块论统通密刘易践围木sical Maximum Principle
3.1 The Weak Maximum Principle
3.2 The Strong Maximum Principle
3.3 Apriori Bounds
3.件代势西副太守座象约4 Gradient Estimates for Poisson's Equation
3.5 A Harnack Inequality
3.6 Operators in Divergence Form
Notes
Problems
Chapter 4 Poisson's Equation 白协油毛屋许让械际施and the Newtonian Potential
4.1 Ho洲环被存刚lder Continuity
介齐空 4.2 The Dirichlet Problem for Poisson's Equation
4.3 Holder Estimates for the Second Derivatives
4.4 Eximates at the Boundary
4.5 Holder Estimates for t格资选口目令连望袁he First Derivatives
Notes
察互初钢庆群诗斯Problems
Chapter 5 Banach and Hilbert Spaces
5.1 The Contraction Mapping Principl协态e
5.2 The Method of Continity
5.3 The Fredholm Alternative
5.4 Dual Spaces and Adjoints
5.5 Hilbert Spaces
5.6 The Projection Theorem
5.7 The Riesz Represenation The害orem
5.8 The Lax-Milgram Theorem
5.9 The Fredholm Alternative in Hilbert Spaces
5.10 Weak Compactness
Notes
Problems
Chapter 6 Calssical Solutions; the Schauder App米玉需景各古她roach
Chapter 7 Sobol军伟误初试未ev Spaces
Chapter 8 Generalized Solutiona and reg左易属散文七宜ularity
Chapter 9 Str特势价ong Solutions
Part Ⅱ Quasilinear Equations
Chapter 10 Maximum and Comparison Principles
Chapter 11 Topological Fixed Point Theorems and Their Application
Chapter 12 Equation in Two Varables
Chapter 13 Holder Extimates for the Cradient
Chapter 14 Boundary Gradient Estimates
Chapter 15 Global and Interior Gradient Bounds
Chapter 16 Equations of Mean Curvature Type
Chapter 17 Fully Nonlinear Equations
Bibliography
Epilogue
Subject Index
Notation Index
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