Heisenberg群上具VMO系数的退化椭圆方程的Morrey正则性

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英文篇名：Morrey Regularity for Degenerate Elliptic Equations with VMO Coefficients in the Heisenberg Group 作者：魏娜 英文作者：WEI Na;School of Statistics and Mathematics,Zhongnan University of Economics and Law; 关键词：Heisenberg群 ; Lp正则性 ; Morrey正则性 ; VMO系数 英文关键词：Heisenberg group;;Lpregularity;;Morrey regularity;;VMO coefficient 中文刊名：YISU 英文刊名：Mathematica Applicata 机构：中南财经政法大学统计与数学学院; 出版日期：2014-10-15 出版单位：应用数学 年：2014 期：v.27;No.115 基金：数学天元青年基金(11326153);; 中央高校基本科研业务费专项资金(31541311209) 语种：中文; 页：YISU201404016 页数：9 CN：04 ISSN：42-1184/O1 分类号：126-134

摘要

本文研究Heisenberg群上具有VMO(零平均振荡)系数的非散度型退化椭圆方程.通过证明适当的Sobolev-Poincaré型不等式,建立方程的Lp正则性;然后利用初等方法,得到退化椭圆方程解的Morrey正则性.
        This paper is devoted to the non-divergence degenerate elliptic equation with VMO(Vanishing Mean Oscillation)coefficients in the Heisenberg group.By proving some suitable Sobolev-Poincarétype inequalities,we establish the Lp regularity for the euqation.Furthermore,Morrey regularity for the degenerate elliptic equation is derived by an elementary method.

引文

[1]Calderón A P,Zygmund A.On the existence of certain singular integrals[J].Acta.Math.,1952,88:85-139.
    [2]Lieberman G M.A mostly elementary proof of Morrey space estimates for elliptic and parabolic equations with VMO coefficients[J].J.Funct.Anal.,2003,201:457-479.
    [3]魏娜,钮鹏程.Heisenberg群上奇异积分的Morrey估计及其应用[J].数学学报,2010,53(6):1149-1162.
    [4]TANG Sufang,NIU Pengcheng.Morrey estimates for parabolic nondivergence operators of Hrmander type[J].Rend.Sem.Mat.Univ.Padova,2010,123:91-129.
    [5]WEI Na,NIU Pengcheng,TANG Sufang,etc.Estimates in generalized Morrey spaces for nondivergence degenerate elliptic operators with discontinuous coefficients[J].Rev.R.Acad.Cienc.Exactas Fís.Nat.,Ser.A Mat.,2012,106(1):1-33.
    [6]LU Guozhen.Weighted Poincaréand Sobolev inequalities for vector fields satisfying Hrmander's condition and applications[J].Revista Matematica Iberoamericana,1992,8(3):367-440.
    [7]LU Guozhen.The sharp Poincaréinequality for free vector fields:an endpoint result[J].Revista Mat.Iberoamericana,1994,10(3):453-466.
    [8]Franchi B,LU Guozhen,Wheeden R L.Representation formulas and weighted Poincaréinequalities for Hrmander vector fields[J].Ann Inst Fourier:Grenoble,1995,45:577-604.
    [9]Danielli D,Garofalo N,Phuc N C.Inequalities of Hardy-Sobolev type in Carnot-Carathéodory spaces[G]//Maz'ya V Sobolev Spaces in Mathematics I.International Mathematical Series,Vol.8.New York:Springer,2009.
    [10]Bramanti M,Brandolini L.Lp estimates for uniformly hypoelliptic operators with discontinuous coefficients on homogenous groups[J].Rend.Sem.Mat.Univ.Pol.Torino.,2000,58(4):389-433.
    [11]Folland G B.Subelliptic estimates and function spaces on nilpotent Lie groups[J].Ark.Mat.,1975,13:161-207.
    [12]Bramanti M,Brandolini L.Lpestimates for nonvariational hypoelliptic operators with VMO coefficients[J].Trans.Amer.Math.Soc.,2000,352(2):781-822.
    [13]Gilbarg D,Trudinger N S.Elliptic Partial Differential Equations of Second Order[M].New York,Heidelberg:Springer-Verlag,1977.