Hardy–Poincaré type inequalities derived from p-harmonic problems

Abstract

We apply general Hardy type inequalities, recently obtained by the author. As a consequence we obtain the family of Hardy—Poincare inequalities with certain constants, contributing to the question about precise constants in such inequalities posed in [2]. We confirm optimality of some constants obtained in [2] and [10]. Furthermore, we give constants for generalized inequalities with the proof of their optimality.