Weighted Hardy Type inequalities with Robin Boundary Conditions

TL;DR

This paper establishes weighted Hardy inequalities for the p-Laplace operator with Robin boundary conditions and explores related inequalities with boundary terms, providing concrete examples and applications in mathematical analysis.

Contribution

It introduces a general weighted Hardy inequality for the p-Laplace operator with Robin boundary conditions and illustrates its applications with concrete examples.

Findings

Derived a general weighted Hardy inequality for p-Laplace with Robin boundary conditions

Provided concrete examples for different weight functions

Extended results to Heisenberg-Pauli-Weyl type inequalities with boundary terms

Abstract

In this paper, we establish a general weighted Hardy type inequality for the $% p-$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 $\mathbb{R}^n$.