幾類與Heisenberg群相關(guān)的函數(shù)空間和變分問題研究.pdf

1、南京理工大學(xué)博士學(xué)位論文幾類與Heisenberg群相關(guān)的函數(shù)空間和變分問題研究姓名：賈高申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：系統(tǒng)工程非線性分析及其應(yīng)用指導(dǎo)教師：楊孝平20030101AbstractThemainaimofthisthesisiStostudythepropertiesofthemapsforHeisenberggrouptarget，whichincludeLipschitzandHOldercontinuity上9(Q，H”)

2、，形119(Q，H“)，BMOandJohnNirenbergestimates，embeddedtheorems，Poincar垂inequalitiesandreversePoincar6inequalities，theregularitiesabouttheminimizersInthelastpart，westudytheexistenceofthesolutionsforsemilinearsubellipticequatio

3、nsandtheestimatesoftheeigenvaluesforsubellipticoperatorsonH“Theresultsaregeneralizationsfortheappropriateones013R“InChapterlwerecallthedefinitionsfortheHeisenberggroupH”，statesomepropertiesingeometryandanalysisandinHolde

4、rcontinuousmapsforHeisenberggrouptargetsInChapter2，westudythepropertiesofP(Q，H”)andw1。(Q，H“)，theprenormandprewealdycompactnessonⅣIp(Q，it“)，BMO(n，H”)andJohn—NirenbergtypeestimateInChapter3，westateandprovesomePoincar6inequ

5、alitiesandreversePoincar6inequalitiesOn也eHeisenberggroupInchapter4，westateandproveCampanatotypeTheorem，MorreytypeTheoremandsomeembeddingTheoremsforthemaps，InChapter5，wefirstrecallsomeresultsoftheexistenceandregularityabo

6、uttheminimizers。SecondlywestudytheEulerequationsaboutthevariationalsandtheapproximateproblemsabouttheminimizersInchapter6，westudyexistenceoftheweaksolutionsforaclassofthenonlinearDirichletproblemsonH“andestimatesoftheeig