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：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

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.

引用

页码：1511 / 1588

页数：78

共 89 条

[1] Aleksandrov A D., 1938, Mat Sb, V3, P27
[2] Aleksandrov A. D., 1939, Mat Sb (NS), V6, P167
[3] Andrews B, 2003, J AM MATH SOC, V16, P443
[4] Gauss curvature flow: the fate of the rolling stones
Andrews, B
[J]. INVENTIONES MATHEMATICAE, 1999, 138 (01) : 151 - 161
[5] [Anonymous], 1985, Springer Series in Soviet Mathematics, DOI DOI 10.1007/978-3-662-09922-3
[6] [Anonymous], 1993, Convex Bodies: The Brunn-Minkowski Theory
[7] Concavity properties for elliptic free boundary problems (vol 71, pg 4461, 2009)
Bianchini, Chiara
Salani, Paolo
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (7-8) : 3551 - 3551
[8] Böröczky KJ, 2013, J AM MATH SOC, V26, P831
[9] GREENIAN POTENTIALS AND CONCAVITY
BORELL, C
[J]. MATHEMATISCHE ANNALEN, 1985, 272 (01) : 155 - 160
[10] BORELL C, 1984, ANN SCI ECOLE NORM S, V17, P451

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