Hardy inequalities for Robin Laplacians

TL;DR

This paper establishes Hardy inequalities for Laplace operators with Robin boundary conditions, detailing their dependence on boundary coefficients for convex domains and exploring extensions to non-convex and unbounded domains.

Contribution

It introduces Hardy inequalities for Robin Laplacians, explicitly characterizing the Hardy weight for convex domains and extending results to more general domains.

Findings

Hardy inequality established for Robin Laplacians

Explicit Hardy weight dependence on boundary coefficient for convex domains

Extensions to non-convex and unbounded domains

Abstract

In this paper we establish a Hardy inequality for Laplace operators with Robin boundary conditions. For convex domains, in particular, we show explicitly how the corresponding Hardy weight depends on the coefficient of the Robin boundary conditions. We also study several extensions to non-convex and unbounded domains.