The Generalized Davies Problem for Polyharmonic Operators

被引：0

作者：

F. G. Avkhadiev

机构：

[1] Kazan (Volga Region) Federal University,

来源：

Siberian Mathematical Journal | 2017年 / 58卷

关键词：

polyharmonic operator; Rellich-type inequality; distance;

D O I：

暂无

中图分类号：

学科分类号：

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：10

共 6 条

[1]

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[2]

Avkhadiev F. G.(2014)A geometric description of domains whose Hardy constant is equal to 1/4 Izv. Math. 78 855-876

[3]

Avkhadiev F. G.(2014)Sharp estimates of Hardy constants for domains with special boundary properties Russian Math. (Iz. VUZ) 58 58-61

[4]

Shafigullin I. K.(2016)Hardy–Rellich inequalities in domains of the Euclidean space J. Math. Anal. Appl. 442 469-484

[5]

Avkhadiev F. G.(1999)The Hardy–Rellich inequality for polyharmonic operators Proc. Royal Soc. Edinburgh 129A 825-839

[6]

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