Weighted Hardy Type inequalities with Robin Boundary Conditions

Abstract

In this paper, we establish a general weighted Hardy type inequality for the Laplace operator with Robin boundary condition. We provide various concrete examples to illustrate our results for different weights. Furthermore, we present some Heisenberg-Pauli-Weyl type inequalities with boundary terms on balls with radius $R$ at the origin in ${\mathbb{R}}^n$.

13 pages, typos corrected, more corollaries and references have been added