Elements of Nonlinear Analysis

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1、ContentsPreface....................................Chapter1.SomePhysicalMotivations...................................11.1.Anelementarytheoryofelasticity11.2.Aprobleminbiology.91.3.Rxercises14Chapter2.AShortBackgroundinFunctionalAnalysis...................

2、152.1.Anintroductiontodistributions152.2.Integrationonboundaries182.3.IntroductiontoSobolevspaces212.4.Exercises37Chapter3.EllipticLinearProblems......................................393.1.TheDirichletproblem393.2.TheLax-Milgramtheoremanditsapplications413

3、.3-Exercises48Chapter4.EllipticVariationalInequalities..............................494.1.AgeneralizationoftheLax-Milgramtheorem494.2.Someapplications.524.3.Exercises58Chapter5.NonlinearEllipticProblems..................................595.1.Acompactnessme

4、thod595.2.Amonotonicitymethod625.3.Ageneralizationofvariationalinequalities665.4.Somemultivaluedproblems715.5.Exercises82Chapter6.ARegularityTheoryforNonlocalVariationalInequalities.........................856.1.Somegeneralresults856.2.Applicationstosecond

5、ordervariationalinequalities916-3-Exercises94Chapter7.UniquenessandNonuniquenessIssues........................957.1.Uniquenessresultforlocalnonlinearproblems.957.2.Nonuniguenessissues.9973.Exercises.102viContentsChapter8.FiniteElementMethodsforEllipticProb

6、lems................1058.1.Anabstractsetting1058.2.Somesimplefiniteelements1068.3.Interpolationerror1138.4.Convergenceresults1168.5.Approximationofnonlinearproblems1228.6.Exercises..........................................................129Chapter9.Minime

7、rs...................................................1319.1.Introduction......................................................1319.2.Thedirectmethod................................................1339.3.Applications.........................................

8、.............1359.4.TheEulerEquation...............................................1429.5.Exercises..........................................................143Chapter10.MinimizingSequences...................