变分法（第4版）

图书标准信息

• 作者 [瑞士]Michael Struwe 编
• 出版社 世界图书出版公司
• 出版时间 2012-03
• 版次 4
• ISBN 9787510042874
• 定价 38.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 302页
• 正文语种 英语

【内容简介】

《变分法（第4版）》是《变分法》第四版，主要讲述在非线性偏微分方程和哈密顿系统中的应用，继第一版出版十八年再次全新呈现。整《变分法（第4版）》都做了大量的修改，仅500多条参考书目就将其价值大大提升。第四版中主要讲述变分微积分，增加了该领域的最新进展。这也是一部变分法学习的教程，特别讲述了yamabe流的收敛和胀开现象以及最新研究发现的调和映射和曲面中热流的向后小泡形成。

【目录】

ChapterI.thedirectmethodsinthecalculusofvariations
1.lowersemi-continuity
degenerateellipticequations
-minimalpartitioninghypersurfaces
-minimalhypersurfacesinriemannianmanifolds
-agenerallowersemi-continuityresult
2.constraints
semilinearellipticboundaryvalueproblems
-perron'smethodinavariationalguise
-theclassicalplateauproblem
3.compensatedcompactness
applicationsinelasticity
-convergenceresultsfornonlinearellipticequations
-hardyspacemethods
4.theconcentration-compactnessprinciple
existenceofextremalfunctionsforsobolevembeddings
5.ekeland'svariationalprinciple
existenceofminimizersforquasi-convexfunctionals
6.duality
hamiltoniansystems
-periodicsolutionsofnonlinearwaveequations
7.minimizationproblemsdependingonparameters
harmonicmapswithsingularities

ChapterⅡ.minimaxmethods
1.thefinitedimensionalcase
2.thepalais-smalecondition
3.ageneraldeformationlemma
pseudo-gradientflowsonbanachspaces
-pseudo-gradientflowsonmanifolds
4.theminimaxprinciple
closedgeodesicsonspheres
5.indextheory
krasnoselskiigenus
-minimaxprinciplesforevenfunctional
-applicationstosemilinearellipticproblems
-generalindextheories
-ljusternik-schnirelmancategory
-ageometricalsi-index
-multipleperiodicorbitsofhamiltoniansystems
6.themountainpasslemmaanditsvariants
applicationstosemilinearellipticboundaryvalueproblems
-thesymmetricmountainpasslemma
-applicationtosemilinearequa-tionswithsymmetry
7.perturbationtheory
applicationstosemilinearellipticequations
8.linking
applicationstosemilinearellipticequations
-applicationstohamil-toniansystems
9.parameterdependence
10.criticalpointsofmountainpasstype
multiplesolutionsofcoerciveellipticproblems
11.non-differentiablefhnctionals
12.ljnsternik-schnirelmantheoryonconvexsets
applicationstosemilinearellipticboundaryvalueproblems

ChapterⅢ.Limitcasesofthepalais-smalecondition
1.pohozaev'snon-existenceresult
2.thebrezis-nirenbergresult
constrainedminimization
-theunconstrainedcase：localcompact-ness
-multiplesolutions
3.theeffectoftopology
aglobalcompactnessresult,184-positivesolutionsonannular-shapedregions,190
4.theyamabeproblem
thevariationalapproach
-thelocallyconformallyflatcase
-theyamabeflow
-theproofoftheorem4.9（followingye[1]）
-convergenceoftheyamabeflowinthegeneralcase
-thecompactcaseucc
-bubbling：thecasu
5.thedirichletproblemfortheequationofconstantmeancurvature
smallsolutions
-thevolumefunctional
-wente'suniquenessresult
-localcompactness
-largesolutions
6.harmonicmapsofriemanniansurfaces
theeuler-lagrangeequationsforharmonicmaps
-bochneridentity
-thehomotopyproblemanditsfunctionalanalyticsetting
-existenceandnon-existenceresults
-theheatflowforharmonicmaps
-theglobalexistenceresult
-theproofoftheorem6.6
-finite-timeblow-up
-reversebubblingandnonuniqueness

appendixa
sobolevspaces
-hslderspaces
-imbeddingtheorems
-densitytheorem
-traceandextensiontheorems
-poincar4inequality
appendixb
schauderestimates
-lp-theory
-weaksolutions
-areg-ularityresult
-maximumprinciple
-weakmaximumprinciple
-application
appendixc
frechetdifferentiability
-naturalgrowthconditions
references
index