Hadamard variational formulas for p-torsion and p-eigenvalue with applications

被引：14

作者：

Huang, Yong ^{[1
]}

Song, Changzhen ^{[2
]}

Xu, Lu ^{[1
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

[2] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China

来源：

GEOMETRIAE DEDICATA | 2018年 / 197卷 / 01期

关键词：

Hadamard variational formula; p-Laplacian equation; Symmetry; Brunn-Minkowski inequality; Minkowski problem; 35J92; 35N25; BRUNN-MINKOWSKI INEQUALITY; OVERDETERMINED PROBLEMS; CONVEX DOMAINS; SYMMETRY; CAPACITY; REGULARITY; UNIQUENESS; LAPLACIAN; LIPSCHITZ; OPERATOR;

D O I：

10.1007/s10711-018-0318-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we pose two kinds of Minkowski problems involving the p-Laplacian operator. The Hadamard variational formulas for some p-Laplacian functionals are obtained. A good application is to prove symmetry results for solutions to some overdetermined problems of p-Laplacian equations.

引用

页码：61 / 76

页数：16

共 31 条

[1] Alexandrov A.D., 1996, SELECTED WORKS 1, V4
[2] A direct uniqueness proof for equations involving the p-Laplace operator
Belloni, M
Kawohl, B
[J]. MANUSCRIPTA MATHEMATICA, 2002, 109 (02) : 229 - 231
[3] Brock F., 2002, REND CIRC MAT PALERM, V51, P375
[4] REGULARITY OF SOLUTION OF N-DIMENSIONAL MINKOWSKI PROBLEM
CHENG, SY
YAU, ST
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1976, 29 (05) : 495 - 516
[5] The Hadamard variational formula and the Minkowski problem for p-capacity
Colesanti, A.
Nystrom, K.
Salani, P.
Xiao, J.
Yang, D.
Zhang, G.
[J]. ADVANCES IN MATHEMATICS, 2015, 285 : 1511 - 1588
[6] The Brunn-Minkowski inequality for p-capacity of convex bodies
Colesanti, A
Salani, P
[J]. MATHEMATISCHE ANNALEN, 2003, 327 (03) : 459 - 479
[7] Colesanti A., 1994, APPL ANAL, V55, P207
[8] Colesanti A., 2006, APPL ANAL, V85, P45, DOI DOI 10.1080/00036810500277819
[9] The Minkowski Problem for Torsional Rigidity
Colesanti, Andrea
Fimiani, Michele
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2010, 59 (03) : 1013 - 1039
[10] Variational formula and overdetermined problem for the principle eigenvalue of k-Hessian operator
Dai, Qiuyi
Shi, Feilin
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (11) : 4136 - 4148

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