The Hadamard variational formula and the Minkowski problem for p-capacity

被引：67
|
作者：
Colesanti, A. [1 ]
Nystrom, K. [3 ]
Salani, P. [1 ]
Xiao, J. [4 ]
Yang, D. [2 ]
Zhang, G. [2 ]
机构：
[1] Univ Dini, Dipartimento Matemat, Viale Morgagni 67-A, I-50134 Florence, Italy
[2] NYU, Polytech Inst, Dept Math, MetroTech Ctr 6, Brooklyn, NY 11201 USA
[3] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden
[4] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
来源：
ADVANCES IN MATHEMATICS | 2015年 / 285卷
基金：
美国国家科学基金会; 加拿大自然科学与工程研究理事会;
关键词：
p-capacity; p-equilibrium potential; p-Laplacian; p-capacitary measure; Convex domain; Variational formula; Minkowski problem; Minkowski inequality; Monge-Ampere equation; Uniqueness; Existence; Regularity; FREE-BOUNDARY REGULARITY; BRUNN-MINKOWSKI; HARMONIC-FUNCTIONS; 2-PHASE PROBLEMS; FIREY THEORY; SOBOLEV; INEQUALITIES; AFFINE; LIPSCHITZ; EQUATIONS;
D O I：
10.1016/j.aim.2015.06.022
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A Hadamard variational formula for p-capacity of convex bodies in R-n is established when 1 < p < n. The formula is applied to solve the Minkowski problem for p-capacity which involves a degenerate Monge Ampere type equation. zkiniqueness for the Minkowski problem for p-capacity is established when 1 < p < n and existence and regularity when 1 < p < 2. These results are (non-linear) extensions of the now classical solution of Jerison of the Minkowski problem for electrostatic capacity (p = 2). (C) 2015 Elsevier Inc. All rights reserved.
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页码：1511 / 1588
页数：78
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