偏微分方程导论

作者简介

《偏微分方程导论(第2版)(英文版)》内容简介：In 1975 I gave a course in partial difierential equations（PDE）at the Uni-versity of Washington to an audience consisting of graduate students whohad taken the standard first-year analysis courses but who had 1ittle back-ground in PDE.Accordingly.it focused on basic classical results in PDEbut aimed in the direction of the recent developments and made fairly ft。eeuse of the techniques of real and complex analysis.The roughly polishednotes for that course constituted the first edition of this book，which hasenjoyed some SUCCESS for the past two decades as a“modern”introductionto PDE.From time to time，however，my conscience ha.S nagged me tomake some revisions——to clean some things up，add more exercises，andinclude some material on pseudodifferential operators.

书籍目录

PREFACEChapter 0PRELIMINARIESA．Notations and DefinitionsB．Results from Advanced CalculusC．ConvolutionsD．The Fourier TransformE．DistributionsF．Compact OperatorsChapter 1LOCAL EXISTENCE THEoRyA．Basic ConceptsB．Real First Order EquationsC．The General Cauchy ProblemD．The Cauchy-Kowalevski TheoremE．Local Solvability：the Lewy ExampleF．Constant-Coefficient Operators：Fundamental SolutionsChapter 2THE LAPLACE oPERATORA．Symmetry Properties of the LaplacianB．Basic Properties of Harmonic FunotionsC．The Fundamental SolutionD．The Dirichlet and Neumann ProblemsE．The Green’S FunctionF．Dirichlet’S PrincipleG．The Dirichlet Problem in a Half-SpaceH．The Dirichlet Problem in a BallI．More about Harmonic FunctionsChapter 3LAYER PoTENTIALSA．The SetupB．Integral OperatorsC．Double Layer PotentialsD．Single Layer PotentialsE．Solution of the ProblemsF．Further RemarksChapter 4THE HEAT oPERAToRA．The Gaussian KernelB．Funotions of the LaplacianC．The Heat Equation in Bounded DomainsChapter 5THE WAVE oPERAToRA．The Cauchy ProblemB．Solution of the Cauchy ProblemC．The Inhomogeneous EquationD．Fourier Analysis of the Wave OperatorE．The Wave Equation in Bounded DomainsF．The Radon TransformChapter 6THE L2 THEOR．Y oF DERIVATIVESA．Sobolev Spaces on RB．Further Results on Sobolev SpacesC．Local Regularity of Elliptic OperatorsD．Constant-Coefficient Hypoelliptic OperatorsE．Sobolev Spaces on Bounded DomainsChapter 7ELLIPTIC BoUNDARY VALUE PRoBLEMSA．Strong EllipticityB．On Integration by PartsC．Dirichlet Forms and Boundary ConditionsD．The Coercive EstimateE．Existence，Uniqueness，and EigenvaluesF．Regularity at the Boundary：the Second Order CaseG．Further Resuits and TechniquesH．Epilogue：the Return of the Green’S FunctionChapter 8PSEUDODIFFERENTIAL OPERATORSA．Basic Definitions and PropertiesB．Kernels of Pseudodifferential OperatorsC．Asymptotic Expansions of SymbolsD．Amplitudes，Adjoints，and ProductsE．Sobolev EstimatesF．Elliptic OperatorsG．Introduction to Microlocal AnalysisH．Change of CoordinatesBIBLIOGRAPHYINDEX OF SYMBOLSINDEX

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《偏微分方程导论(第2版)(英文版)》是由世界图书出版公司出版的。

内容概要

作者：（美国）福兰德（Gerald B.Folland）

章节摘录

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