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

doi:10.1016/S0252-9602(09)60092-8

数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1143-1154.doi: 10.1016/S0252-9602(09)60092-8

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

胡华香, 周树清

Department of Mathematics, Hunan Normal University, hangsha |410081, China

收稿日期:2008-05-25 修回日期:2009-03-30 出版日期:2009-09-20 发布日期:2009-09-20
通讯作者: Zhou Shuqing E-mail:hunanhhx@163.com; zhoushuqing87@163.com

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

HU Hua-Xiang, ZHOU Shu-Qing

Department of Mathematics, Hunan Normal University, hangsha |410081, China

Received:2008-05-25 Revised:2009-03-30 Online:2009-09-20 Published:2009-09-20
Contact: Zhou Shuqing E-mail:hunanhhx@163.com; zhoushuqing87@163.com
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)

摘要/Abstract

摘要：

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

关键词: PLaplacian, energy integral, runn Minkowski type inequlity

Abstract:

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

中图分类号:

35J20

胡华香, 周树清. BRUNN-MINKOWSKI INEQUALITY FOR VARIATIONAL FUNCTIONAL INVOLVING THE P-LAPLACIAN OPERATOR[J]. 数学物理学报(英文版), 2009, 29(5): 1143-1154.

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.

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

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

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