Hardy–Poincaré type inequalities derived from $p$-harmonic problems
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 . We confirm optimality of some constants obtained in  and . Furthermore, we give constants for generalized inequalities with the proof of their optimality.