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[美] 泰勒 (Taylor M.E.) 著 / 世界图书出版公司 / 2014-01 / 平装
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偏微分方程(第3卷)(第2版)
Partialdifferentialequationsisamany-facetedsubject.Createdtodescribethemechanicalbehaviorofobjectssuchasvibratingstringsandblowingwinds,ithasdevelopedintoabodyofmaterialthatinteractswithmanybranchesofmath-ematics,suchasdifferentialgeometry,complexanalysis,andharmonicanalysis,aswellasaubiquitousfactorinthedescriptionandelucidationofproblemsinmathematicalphysics.
ContentsofVolumesIandⅡPreface13FunctionSpaceandOperatorTheoryforNonlinearAnalysis1Lp-Sobolevspaces2Sobolevimbeddingtheorems3Gagliardo-Nirenberg-Moserestimates4Trudinger'sinequalities5SingularintegraloperatorsonLp6ThespacesHs,p7IP-spectraltheoryoftheLaplaceoperator8HolderspacesandZygmundspaces9Pseudodifferentialoperatorswithnonregularsymbols10Paradifferentialoperators11Youngmeasuresandfuzzyfunctions12HardyspacesAVariationsoncomplexinterpolatioReferences14NonlinearEllipticEquations1Aclassofsemilinearequations2Surfaceswithnegativecurvature3Localsolvabilityofnonlinearellipticequations4EllipticregularityI(interiorestimates)5IsometricimbeddingofRiemannianmanifolds6Minimalsurfaces6BSecondvariationofarea7Theminimalsurfaceequation8EllipticregularityII(boundaryestimates)9EllipticregularityIII(DeGiorgi-Nash-Mosertheory)10TheDirichletproblemforquasi-linearellipticequations11Directmethodsinthecalculusofvariations12Quasi-linearellipticsystems12BFurtherresultsonquasi-linearsystems13EllipticregularityIV(Krylov-Safonovestimates)14Regularityforaclassofcompletelynonlinearequations15Monge-Ampereequations16EllipticequationsintwovariablesAMorreyspacesBLeray-Schauderfixed-pointtheoremsReferences15NonlinearParabolicEquations1Semilinearparabolicequations2Applicationstoharmonicmaps3Semilinearequationsonregionswithboundary4Reaction-diffusionequations5AnonlinearTrotterproductformula6TheStefanproblem7Quasi-IinearparabolicequationsI8Quasi-linearparabolicequationsII(sharperestimates)9Quasi-IinearparabolicequationsIII(Nash-Moserestimates)References16NonlinearHyperbolicEquations1Quasi-Iinear,symmetrichyperbolicsystems2Symmetrizablehyperbolicsystems3Second-orderandhigher-orderhyperbolicsystems4EquationsinthecomplexdomainandtheCauchyKowalewskytheorem5Compressiblefiuidmotion6Weaksolutionstoscalarconservationlaws;theviscositymethod7Systemsofconservationlawsinonespacevariable;Riemannproblems8Entropy-fluxpairsandRiemanninvariants9Globalweaksolutionsofsome2x2systems10VibratingstringsrevisitedReferences17EulerandNavier-StokesEquationsforlncompressibleFluids1Euler'sequationsforidealincompressiblefluidflow2ExistenceofsolutionstotheEulerequations3Eulerflowsonboundedregions4Navier-Stokesequations5Viscousflowsonboundedregions6Vanishingviscositylimits7FromvelocityfieldconvergencetofiowconvergenceARegularityfortheStokessystemonboundeddomainsReferences18Einstein'sEquationsIndex
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