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

被引：7
作者：
Hu Huaxiang [1 ]
Zhou Shuqing [1 ]
机构：
[1] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2009年 / 29卷 / 05期
关键词：
P-Laplacian; energy integral; Brunn-Minkowski type inequlity; BOUNDARY-VALUE PROBLEMS; LOG-CONCAVE FUNCTIONS; GEOMETRIC INEQUALITIES; CONVEX-BODIES; REGULARITY; EQUATIONS; CAPACITY; DOMAINS;
D O I：
10.1016/S0252-9602(09)60092-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we investigate the following elliptic problem involving the P-Laplacian (P) { -Div(vertical bar del u vertical bar(p-2)del u) = vertical bar u vertical bar(q-1)u in K, u > 0 in K, u = 0 on partial derivative K, where p > 1, 0 < q < p - 1, K subset of R-n with (K) over bar is an element of K-n, and prove that the energy integral of the problem (P) satisfies a Brunn-Minkowski type inequality.
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页码：1143 / 1154
页数：12
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