Sharp second order inequalities with distance function to the boundary and applications to a p-Biharmonic singular problem
Analysis of PDEs
2025-07-04 v1
Abstract
In this paper, we prove generalizations to the L^p setting of the Hardy-Rellich inequalities on domains of R^N with singularity given by the distance function to the boundary. The inequalities we obtain are either sharp in bounded domains, where we provide concrete minimizing sequences, or give a new bound for the sharp constant, while also depending on the geometric properties of the domain and its boundary. We also give applications to the existence and non-existence of solutions for a singular problem using variational methods and a Pohozaev identity.
Cite
@article{arxiv.2507.02551,
title = {Sharp second order inequalities with distance function to the boundary and applications to a p-Biharmonic singular problem},
author = {Cristian Cazacu and Teodor Rugină},
journal= {arXiv preprint arXiv:2507.02551},
year = {2025}
}