The Generalized Davies Problem for Polyharmonic Operators

被引：6

作者：

Avkhadiev, F. G. ^{[1
]}

机构：

[1] Kazan Volga Reg Fed Univ, Kazan, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2017年 / 58卷 / 06期

基金：

俄罗斯基础研究基金会;

关键词：

polyharmonic operator; Rellich-type inequality; distance; RELLICH INEQUALITIES; DOMAINS;

D O I：

10.1134/S0037446617060027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Davies problem is connected with the maximal constants in Hardy-type inequalities. We study the generalizations of this problem to the Rellich-type inequalities for polyharmonic operators in domains of the Euclidean space. The estimates are obtained solving the generalized problem under an additional minimal condition on the boundary of the domain. Namely, for a given domain we assume the existence of two balls with sufficiently small radii and the following property: the balls have only a sole common point; one ball lies inside the domain and the other is disjoint from the domain.

引用

页码：932 / 942

页数：11

共 10 条

[1]

[Anonymous], 1985, Appl. Math. Sci.

[2]

[Anonymous], 2010, Lecture Notes in Mathematics

[3] Rellich inequalities for polyharmonic operators in plane domains [J].