An end-point global gradient weighted estimate for quasilinear equations in non-smooth domains

TL;DR

This paper develops a new weighted gradient estimate for quasilinear elliptic equations in non-smooth Reifenberg flat domains, extending results to Lorentz-Morrey spaces below the natural exponent.

Contribution

It introduces an end-point global gradient estimate with $A_1$ weights for solutions in non-smooth domains, advancing the understanding of gradient regularity.

Findings

Weighted norm inequality at the natural exponent for gradients

Gradient estimates in Lorentz-Morrey spaces below the natural exponent

Extension of regularity results to Reifenberg flat domains

Abstract

A weighted norm inequality involving $A_1$ weights is obtained at the natural exponent for gradients of solutions to quasilinear elliptic equations in Reifenberg flat domains. Certain gradient estimates in Lorentz-Morrey spaces below the natural exponent are also obtained as a consequence of our analysis.