偏微分方程（第3卷）（第2版）
作者:
[美] 泰勒
（Taylor M.E.） 著
出版时间:
2014-01
版次:
2
ISBN:
9787510068157
定价:
109.00
装帧:
平装
开本:
24开
纸张:
胶版纸
页数:
715页
正文语种:
英语
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Partialdifferentialequationsisamany-facetedsubject.Createdtodescribethemechanicalbehaviorofobjectssuchasvibratingstringsandblowingwinds，ithasdevelopedintoabodyofmaterialthatinteractswithmanybranchesofmath-ematics，suchasdifferentialgeometry，complexanalysis，andharmonicanalysis，aswellasaubiquitousfactorinthedescriptionandelucidationofproblemsinmathematicalphysics. ContentsofVolumesIandⅡ
Preface
13FunctionSpaceandOperatorTheoryforNonlinearAnalysis
1Lp-Sobolevspaces
2Sobolevimbeddingtheorems
3Gagliardo-Nirenberg-Moserestimates
4Trudinger'sinequalities
5SingularintegraloperatorsonLp
6ThespacesHs,p
7IP-spectraltheoryoftheLaplaceoperator
8HolderspacesandZygmundspaces
9Pseudodifferentialoperatorswithnonregularsymbols
10Paradifferentialoperators
11Youngmeasuresandfuzzyfunctions
12Hardyspaces
AVariationsoncomplexinterpolatio
References
14NonlinearEllipticEquations
1Aclassofsemilinearequations
2Surfaceswithnegativecurvature
3Localsolvabilityofnonlinearellipticequations
4EllipticregularityI(interiorestimates)
5IsometricimbeddingofRiemannianmanifolds
6Minimalsurfaces
6BSecondvariationofarea
7Theminimalsurfaceequation
8EllipticregularityII(boundaryestimates)
9EllipticregularityIII(DeGiorgi-Nash-Mosertheory)
10TheDirichletproblemforquasi-linearellipticequations
11Directmethodsinthecalculusofvariations
12Quasi-linearellipticsystems
12BFurtherresultsonquasi-linearsystems
13EllipticregularityIV(Krylov-Safonovestimates)
14Regularityforaclassofcompletelynonlinearequations
15Monge-Ampereequations
16Ellipticequationsintwovariables
AMorreyspaces
BLeray-Schauderfixed-pointtheorems
References
15NonlinearParabolicEquations
1Semilinearparabolicequations
2Applicationstoharmonicmaps
3Semilinearequationsonregionswithboundary
4Reaction-diffusionequations
5AnonlinearTrotterproductformula
6TheStefanproblem
7Quasi-IinearparabolicequationsI
8Quasi-linearparabolicequationsII(sharperestimates)
9Quasi-IinearparabolicequationsIII(Nash-Moserestimates)
References
16NonlinearHyperbolicEquations
1Quasi-Iinear,symmetrichyperbolicsystems
2Symmetrizablehyperbolicsystems
3Second-orderandhigher-orderhyperbolicsystems
4EquationsinthecomplexdomainandtheCauchyKowalewskytheorem
5Compressiblefiuidmotion
6Weaksolutionstoscalarconservationlaws;theviscositymethod
7Systemsofconservationlawsinonespacevariable;Riemannproblems
8Entropy-fluxpairsandRiemanninvariants
9Globalweaksolutionsofsome2x2systems
10Vibratingstringsrevisited
References
17EulerandNavier-StokesEquationsforlncompressibleFluids
1Euler'sequationsforidealincompressiblefluidflow
2ExistenceofsolutionstotheEulerequations
3Eulerflowsonboundedregions
4Navier-Stokesequations
5Viscousflowsonboundedregions
6Vanishingviscositylimits
7Fromvelocityfieldconvergencetofiowconvergence
ARegularityfortheStokessystemonboundeddomains
References
18Einstein'sEquations
Index
-
内容简介:
Partialdifferentialequationsisamany-facetedsubject.Createdtodescribethemechanicalbehaviorofobjectssuchasvibratingstringsandblowingwinds，ithasdevelopedintoabodyofmaterialthatinteractswithmanybranchesofmath-ematics，suchasdifferentialgeometry，complexanalysis，andharmonicanalysis，aswellasaubiquitousfactorinthedescriptionandelucidationofproblemsinmathematicalphysics.
-
目录:
ContentsofVolumesIandⅡ
Preface
13FunctionSpaceandOperatorTheoryforNonlinearAnalysis
1Lp-Sobolevspaces
2Sobolevimbeddingtheorems
3Gagliardo-Nirenberg-Moserestimates
4Trudinger'sinequalities
5SingularintegraloperatorsonLp
6ThespacesHs,p
7IP-spectraltheoryoftheLaplaceoperator
8HolderspacesandZygmundspaces
9Pseudodifferentialoperatorswithnonregularsymbols
10Paradifferentialoperators
11Youngmeasuresandfuzzyfunctions
12Hardyspaces
AVariationsoncomplexinterpolatio
References
14NonlinearEllipticEquations
1Aclassofsemilinearequations
2Surfaceswithnegativecurvature
3Localsolvabilityofnonlinearellipticequations
4EllipticregularityI(interiorestimates)
5IsometricimbeddingofRiemannianmanifolds
6Minimalsurfaces
6BSecondvariationofarea
7Theminimalsurfaceequation
8EllipticregularityII(boundaryestimates)
9EllipticregularityIII(DeGiorgi-Nash-Mosertheory)
10TheDirichletproblemforquasi-linearellipticequations
11Directmethodsinthecalculusofvariations
12Quasi-linearellipticsystems
12BFurtherresultsonquasi-linearsystems
13EllipticregularityIV(Krylov-Safonovestimates)
14Regularityforaclassofcompletelynonlinearequations
15Monge-Ampereequations
16Ellipticequationsintwovariables
AMorreyspaces
BLeray-Schauderfixed-pointtheorems
References
15NonlinearParabolicEquations
1Semilinearparabolicequations
2Applicationstoharmonicmaps
3Semilinearequationsonregionswithboundary
4Reaction-diffusionequations
5AnonlinearTrotterproductformula
6TheStefanproblem
7Quasi-IinearparabolicequationsI
8Quasi-linearparabolicequationsII(sharperestimates)
9Quasi-IinearparabolicequationsIII(Nash-Moserestimates)
References
16NonlinearHyperbolicEquations
1Quasi-Iinear,symmetrichyperbolicsystems
2Symmetrizablehyperbolicsystems
3Second-orderandhigher-orderhyperbolicsystems
4EquationsinthecomplexdomainandtheCauchyKowalewskytheorem
5Compressiblefiuidmotion
6Weaksolutionstoscalarconservationlaws;theviscositymethod
7Systemsofconservationlawsinonespacevariable;Riemannproblems
8Entropy-fluxpairsandRiemanninvariants
9Globalweaksolutionsofsome2x2systems
10Vibratingstringsrevisited
References
17EulerandNavier-StokesEquationsforlncompressibleFluids
1Euler'sequationsforidealincompressiblefluidflow
2ExistenceofsolutionstotheEulerequations
3Eulerflowsonboundedregions
4Navier-Stokesequations
5Viscousflowsonboundedregions
6Vanishingviscositylimits
7Fromvelocityfieldconvergencetofiowconvergence
ARegularityfortheStokessystemonboundeddomains
References
18Einstein'sEquations
Index
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