Two functionals connected to the Laplacian in a class of doubly connected domains on rank one symmetric spaces of non-compact type

被引：6
|
作者：
Chorwadwala, Anisa M. H. [1 ]
Vemuri, M. K. [2 ]
机构：
[1] Indian Inst Sci Educ & Res, Pune 411021, Maharashtra, India
[2] W Virginia Univ, Dept Math, Morgantown, WV 26506 USA
来源：
GEOMETRIAE DEDICATA | 2013年 / 167卷 / 01期
关键词：
Shape optimization problem; Rank one symmetric spaces of non-compact type; Dirichlet boundary value problem;
D O I：
10.1007/s10711-012-9800-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let B (1) be a ball in a non-compact rank-one symmetric space and let B (0) be a smaller ball inside it. It is shown that if y is the solution of the problem -Delta u = 1 in vanishing on the boundary, then the Dirichlet-energy of y is minimal if and only if the balls are concentric. It is also shown that the first Dirichlet eigenvalue of the Laplacian on is maximal if and only if the two balls are concentric. The formalism of Damek-Ricci harmonic spaces is used.
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页码：11 / 21
页数：11
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