Acta mathematica scientia, Series B >
BRUNN-MINKOWSKI INEQUALITY FOR VARIATIONAL FUNCTIONAL INVOLVING THE P-LAPLACIAN OPERATOR
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)
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.
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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