Rellich inequalities for polyharmonic operators in plane domains

被引：7
作者：
Avkhadiev, F. G. [1 ]
机构：
[1] Kazan Fed Univ, Kazan, Russia
来源：
SBORNIK MATHEMATICS | 2018年 / 209卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
Rellich inequality; polyharmonic operator; uniformly perfect set; Poincare metric; EUCLIDEAN-SPACE; HARDY CONSTANT;
D O I：
10.1070/SM8739
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Functionals whose values are defined as sharp constants in Rellich inequalities are investigated for polyharmonic operators in plane domains. The weight function is taken to be a power of the distance of a point to the boundary of the domain. Estimates are obtained for arbitrary domains, as is a test for these constants to be positive, and precise values are found for convex domains and for domains close to convex in a certain sense. The case when the weight function is taken to be a power of the coefficient in the Poincare metric is also treated.
引用
收藏
页码：292 / 319
页数：28
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