The Dirichlet problem in a class of generalized weighted spaces

TL;DR

This paper investigates the continuity of certain integral operators in generalized weighted Morrey spaces and applies these results to analyze the regularity of solutions to the Dirichlet problem for elliptic equations with discontinuous data.

Contribution

It introduces new continuity results for sub-linear integral operators in generalized weighted Morrey spaces and applies them to the Dirichlet problem with discontinuous data.

Findings

Continuity of integral operators in generalized weighted Morrey spaces.

Global regularity results for elliptic equations with discontinuous data.

Estimates linking operator behavior to solution regularity.

Abstract

We show continuity in generalized weighted Morrey spaces of sub-linear integral operators generated by some classical integral operators and commutators. The obtained estimates are used to study global regularity of the solution of the Dirichlet problem for linear uniformly elliptic operators with discontinuous data.