Siberian Mathematical Journal

, Volume 58, Issue 6, pp 932–942 | Cite as

The Generalized Davies Problem for Polyharmonic Operators

  • F. G. Avkhadiev


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.


polyharmonic operator Rellich-type inequality distance 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia

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