偏微分方程（第3卷）（第2版）

图书标准信息

• 作者 [美]泰勒（Taylor M.E.） 著
• 出版社 世界图书出版公司
• 出版时间 2014-01
• 版次 2
• ISBN 9787510068157
• 定价 109.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 715页
• 正文语种 英语

【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