Hardy-Rellich integral inequalities in domains satisfying the exterior sphere condition

Abstract

© 2019 American Mathematical Society. Analogs of Hardy-Rellich inequalities are studied for compactly supported functions on the domains of Euclidean space in the case when weight functions are powers of the distance between a point and the boundary of the domain and the domains satisfy the exterior sphere condition. Explicit estimates of constants in this inequalities are obtained in terms of the dimension, the weight function, and two geometric characteristics: the radius in the exterior sphere condition and the inner radius of the domain.