Global W^1,p regularity for an elliptic problem with measure source and Leray-Hardy potential,

TL;DR

This paper establishes global W^1,p regularity results for elliptic equations involving Leray-Hardy operators with measure sources, using a duality approach in a weighted distributional setting.

Contribution

It introduces a novel duality method to obtain regularity estimates for elliptic problems with measure data and Leray-Hardy potentials.

Findings

Proves global W^1,p estimates for elliptic equations with measure sources.

Develops a duality approach tailored to Leray-Hardy operators.

Extends regularity theory to include measure data in weighted frameworks.

Abstract

In this paper, we develop the Littman-Stampacchia-Weinberger duality approach to obtain global W^1,p estimates for a class of elliptic problems involving Leray-Hardy operators and measure sources in a distributional framework associated with a dual formulation with a specific weight function.