Hardy–Poincaré type inequalities derived from $p$-harmonic problems
Volume 101 / 2014
Banach Center Publications 101 (2014), 225-238
MSC: Primary 26D10; Secondary 26D15, 35J60, 35R45.
DOI: 10.4064/bc101-0-17
Abstract
We apply general Hardy type inequalities, recently obtained by the author. As a consequence we obtain a family of Hardy–Poincaré inequalities with certain constants, contributing to the question about precise constants in such inequalities posed in [3]. We confirm optimality of some constants obtained in [3] and [8]. Furthermore, we give constants for generalized inequalities with the proof of their optimality.
