带有Bessel位势的积分方程正解的对称性和正则性-论文.pdf

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1、第32卷第2期江苏师范大学学报(自然科学版)VolI32，No．22014年6月JournalofJiangsuNormalUniversity(NaturalScienceEdition)Jun．，2014ArticleID：2095-4298(2014)02—0035-08SymmetryandregularityofpositivesolutionstosomesystemassociatedwithBesselpotentialsChenWu(SchoolofMathematics8LStatistics，Jiang

2、suNormalUniversity，Xuzhou221116，Jiangsu，China)Abstract：ThesymmetryandregularityofpositivesolutionstoanintegralsysteminvolvingBesselpotentialsarecon—cernedinthispaper．Byusingthemethodofmovingplanes，itisprovedthatthepositivesolutionsareradialsym—metric．Byusingtworegu

3、larityliftinglemmas，theregularityforintegrablesolutionsarestudied．ItisfirstlyliftedtoL。。andthentoLipsehitzcontinuous．Keywords：regularitylifting；Besselpotential；radialsymmetry；Lestimate；LipschitzcontinuousCLCnumber：O175．3Documentcode：Adoi：10．3969／j．issn．2095-4298．20

4、14．02．008带有Bessel位势的积分方程正解的对称性和正则性陈武(江苏师范大学数学与统计学院，江苏徐州221116)摘要：考虑带有贝塞尔位势的积分方程的正解的对称性和正则性，通过动平面方法证明正解是径向对称的．应用正则性提升引理，将正解先提升至L。。，再提升至Lipschitz连续．关键词：正则性提升；Bessel位势；径向对称性；L估计；Lipschitz连续obtainedtheradialsymmetryandmonotonicityresults．0IntroductionRecently．Hanetal[。

5、]appliedtheregularityliftingbyLetusrecallsomesymmetryandregularityre—contractionoperatorstogettheLestimate，andusedsultsofsomePDEsystem．theregularityliftingbycombinationsofcontractionLetubeapositivesolutionofthefollowingandshrinkingoperatorstoprovetheLipschitzcontin

6、u—semilinearpartialdifferentialequationinR”：ityestimate．(I一△)专“一Up，(1)MaandChencontinuedtheirinvestigationinE3]andstudiedthepositivesolutionsofthefollowingwherea>。，户>1’and△一奎i=1翕denOtetheusuaISchr6dingertypesystemofcoupledsemilinearfractionLaplaceoperatorin．Underso

7、meappropriatedecaypartialdifferentialequationsinR：assumptionofthesolutionsatinfinity，equation(1)isf(I一△)u一矿，equivalenttothefollowingintegralequation：I(卜(⋯3)一△)导一=，(2)，where*denotestheconvolutionandgoistheBesselwherea，>0andP，q>1．Theystudiedtheradialkernelwhosedetail

8、edintroductionwillbegiveninthesymmetryandmonotonicityforthepositivesolutionsfollowingsection．ofthissystembyusingthemethodofmovingplaneinMaetalE]e