拟线性次椭圆方程很弱解正则性及一类开口弧上的边值问题

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1、北京交通大学硕士学位论文拟线性次椭圆方程很弱解正则性及一类开口弧上的边值问题姓名：王喜芬申请学位级别：硕士专业：应用数学指导教师：郑神州20080501北京交通大学硕士学位论文ABSTRACTABSTRACT：Thepaperismadeupoftwoparts．Inthefirstpart．ImainlystudytheimprovementofintegraliblityofveryweaksolutionsofquasilinearsubellipticequationsonCarnotgroup．

2、TheHodgedecompositionandestimatesondisturb-ingvectorfieldsaregiven，andaccol‘(1ingtotheconstructionofgeneralizedreverseH61derinequalitybyHodgedecompositionondisturbingvectorfields，wemayobtintheregularityresultoftheveryweaksolutions．Inthesecondpart，Istudyth

3、eprob-lemsofRiemann’boundaryvalueontheopenarc8withinvariantunderthefiniteMSbinstransformationgroupinthecomplexplane．Theresolvabilityofcorrespond-ingproblemispresentedbywayofso-calledCauchytypeintegralandstandardfunctions．Asfollows：Thefirstpart，weshallcons

4、iderveryweaksolutionsofquasilinearsubellipticequationsonCarnotgroup，it’Smadeupofthefirsttwochapter．Inthefirstchapter，webrieflyintroducethedevelopmentoftheveryweaksolutionandfundamentaldefinationofCarnotgroup，moreoverthebackgroundofselectingthisquestion．In

5、thesecondchapter，weshallconsidertheregularityofveryweaksolutiononCarnotgroupforquasilinearsubellipticequationsa8follows．．X+A(x，t‘，Xu)+B(x，t‘，Xu)=0，z∈Qhenceitisaclassicalsolutionof(2．1)．(2．1)Thesecondpart．weshaustudytheproblemsofRiemann’boundaryvalueonthea

6、rcswithinvariantunderthefiniteMSbiustransformationgroup．Itismadeupofthenexttwochapter．Thethirdchapter，weshallpresenttheintroductionthevalueproblemintheclassofanalyticfunctionsandsomeproblems．北京交通大学硕士学位论文Theforthchapter．weshaUinvestigatetheRiemannboundaryv

7、alueprob-lemonthearcswithfinitinvariantMSbiustransformationgroup．Thecorrespond-ingresolvabilitytheoremandaformalsolutionareobtainedbytransformingtheboundaryvalueproblemwithfinitMfbiustransformationgroupintothesolutionofboundaryvalueproblemonthearcwithfund

8、amentalregions．KEYWORLDS：Subellipticoperators；Veryweaksolutions；Carnot-Carathdodory’Sspaces；Hodgedecomposition；M6biustransformationgroup；Riemann’sboundaryvalueCLASSN0：0175．2V学位论文版权使用授权书本学位论文作者完全了解北京交通大学有关保留、使用学位论文的规