On the extrema of Dirichlet's first eigenvalue of a family of punctured regular polygons in two dimensional space forms

被引：5

作者：

Aithal, A. R. ^{[1
]}

Raut, Rajesh

机构：

[1] Univ Bombay, Dept Math, Bombay 400098, Maharashtra, India

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2012年 / 122卷 / 02期

关键词：

Laplace Beltrami operator; extremum of first eigenvalues; Green's identities for polygonal domains; Hadamard formula for polygonal domains;

D O I：

10.1007/s12044-012-0068-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be two regular polygons of n sides in a space form M (2)(kappa) of constant curvature kappa = 0,1 or -aEuro parts per thousand 1 such that and having the same center of mass. Suppose is circumscribed by a circle C contained in We fix and vary by rotating it in C about its center of mass. Put the interior of in M (2)(kappa). It is shown that the first Dirichlet's eigenvalue lambda (1)( Omega) attains extremum when the axes of symmetry of coincide with those of.

引用

页码：257 / 281

页数：25