Laplace-Beltrami算子和Green算子復合作用的范數不等式.pdf

1、哈爾濱工業(yè)大學碩士學位論文LaplaceBeltrami算子和Green算子復合作用的范數不等式姓名：蔣秋梅申請學位級別：碩士專業(yè)：運籌學與控制論指導教師：包革軍20050601AbstractThetheoryofoperatorshasplayedaveryimportantpartinmanyfields，suchasLaplace—Beltramioperator△andGreen’SoperatorGarewidelyused

2、inphysics，partialdifferentialequations，potentialtheoryandharmonicanalysis，etc。ThegradientoperatorVandthehomotopyoperatorTareeffectivetoolsinanalysiswhichhavefoundedmanyapplicationsindifferentaerasofmathematics，includingt

3、opologyanddifferentialgeometry，SOithasimportanttheoreticalandpracticalsignificancesforstudyingtheoperators。Inrecentyears，thestudyofAharmonictentorshasdevelopeddeeplyanddeeplybecauseoftheimportantroleofA—harmonictensorsin

4、potentialtheory，thequasiregularmappingsandthetheoryofelasticity，andmanyinterestingresultshavebeenestablished。Withlucubratingtheweights，peoplenotnolystudythepropertiesandthetraitsoftheA，一weight，爿，(五)一weight，47一weightandSO

5、on，butbegintosetaboutstudyingtheA“(^彳)一twoweights，4主4一tWOweightsetcaInthispaper，wemainlystud)thenorminequalitiesforcompositionsofAandGoperators，obtainthe4l—twoweightnorminequalitiesforcompositionsof△andGoperatorsappliedt

6、OA—harmonictensors。Accordingtothedifferentintegraldomain，wegivethelocalandglobalnorminequalities，thereinto，theglobalnorrninequalitiessplitintotWOcases，oneisdomainoneismanifold。andthensimplyintroducetheFnonTlestimatesandt

7、heSobolev—poincar6embeddingtheoremforthecompositionsofthegradientoperatorV，thehomotopyoperatorLtheLaplaceBeltramioperatorA，Green’SoperatorG。IntermsofthepropertiesandcharacteristicsofV、T、A、Gtenchangetheirsequencesofoperat