The Brunn-Minkowski inequality for p-capacity of convex bodies

被引:75
作者
Colesanti, A [1 ]
Salani, P [1 ]
机构
[1] Univ Florence, Dipartimento Matemat U Dini, I-50134 Florence, Italy
关键词
REGULARITY;
D O I
10.1007/s00208-003-0460-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we prove the Brunn-Minkowski inequality for the p-capacity of convex bodies (i.e convex compact sets with non-empty interior) in R-n, for every p is an element of (1, n). Moreover we prove that the equality holds in such inequality if and only if the involved bodies coincide up to a translation and a dilatation.
引用
收藏
页码:459 / 479
页数:21
相关论文
共 19 条
[1]   Convex viscosity solutions and state constraints [J].
Alvarez, O ;
Lasry, JM ;
Lions, PL .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1997, 76 (03) :265-288
[2]   RADIAL AVERAGING TRANSFORMATIONS AND GENERALIZED CAPACITIES [J].
BANDLE, C ;
MARCUS, M .
MATHEMATISCHE ZEITSCHRIFT, 1975, 145 (01) :11-17
[3]  
BONNESEN T, 1934, THEORIE CONVEXER KOR
[4]  
BORELL C, 1984, ANN SCI ECOLE NORM S, V17, P451
[5]   CAPACITARY INEQUALITIES OF THE BRUNN-MINKOWSKI TYPE [J].
BORELL, C .
MATHEMATISCHE ANNALEN, 1983, 263 (02) :179-184
[6]   CONVEXITY PROPERTIES OF SOLUTIONS TO SOME CLASSICAL VARIATIONAL-PROBLEMS [J].
CAFFARELLI, LA ;
SPRUCK, J .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1982, 7 (11) :1337-1379
[7]   On the case of equality in the Brunn-Minkowski inequality for capacity [J].
Caffarelli, LA ;
Jerison, D ;
Lieb, EH .
ADVANCES IN MATHEMATICS, 1996, 117 (02) :193-207
[8]  
CHITI G, 1992, INT S NUM M, V103, P109
[10]  
Evans L.C., 2015, MEASURE THEORY FINE