Sharp Second Order Inequalities with Distance Function to the Boundary and Applications to a p -Biharmonic Singular Problem
Abstract
Abstract. In this paper, we prove generalizations to the [Formula: see text]-setting of the Hardy–Rellich inequalities on domains of [Formula: see text] with singularity given by the distance function to the boundary. The inequalities we obtain either are 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 nonexistence of solutions for a singular problem using variational methods and a Pohozaev identity.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Mathematical Inequalities and Applications
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 1
- Pages
- 206–237
- Publication date
- 8 January 2026
- Language
- EN