Articles

BRUNN-MINKOWSKI INEQUALITY FOR VARIATIONAL FUNCTIONAL INVOLVING THE  P-LAPLACIAN OPERATOR

  • HU Hua-Xiang ,
  • ZHOU Shu-Qing
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  • Department of Mathematics, Hunan Normal University, hangsha |410081, China

Received date: 2008-05-25

  Revised date: 2009-03-30

  Online published: 2009-09-20

Supported by

The Project supported by Natural Science Foundation f China (10671064), Scientific Research Fund of Hunan
Provincial Education Department (06C516) and Excellent Youth rogramm of Hunan Normal University (080640)

Abstract

In this paper, we investigate the following elliptic problem involving the P-Laplacian
 (P) {

  -Div(| u|p-2    u) =|u|q-1u  in  K,
  u>0                                    in  K,
  u=0                                    on  ∂K,

where p>1, 0<q<p-1, K     Rn with K ∈ Kn , and prove that the energy integral of the problem (P) satisfies a Brunn-Minkowski type inequality.

Cite this article

HU Hua-Xiang , ZHOU Shu-Qing . BRUNN-MINKOWSKI INEQUALITY FOR VARIATIONAL FUNCTIONAL INVOLVING THE  P-LAPLACIAN OPERATOR[J]. Acta mathematica scientia, Series B, 2009 , 29(5) : 1143 -1154 . DOI: 10.1016/S0252-9602(09)60092-8

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