# Global weighted gradient estimates for nonlinear p-Laplacian type elliptic equations and its application

## TL;DR

This paper establishes global weighted gradient estimates for solutions to nonlinear p-Laplacian type elliptic equations on Reifenberg flat domains, and explores Besov regularity for certain harmonic equations, advancing understanding of regularity in complex geometries.

## Contribution

It provides new global weighted $W^{1,p}$ estimates for nonlinear elliptic equations with specific regularity assumptions on the coefficients, and derives Besov regularity results for special harmonic equations.

## Key findings

- Established global weighted $W^{1,p}$ estimates for nonlinear elliptic equations.
- Proved Besov regularity for solutions of certain harmonic equations.
- Extended regularity theory to Reifenberg flat domains.

## Abstract

We obtain the global weighted $W^{1,p}$ estimates for weak solutions of nonlinear elliptic equations over Reifenberg flat domains. Where nonlinearity $A(x,z,\xi)$ is assumed to be local uniform continuous in $z$ and have small BMO semi-norm in $x$. Moreover, we derive Besov regularity for solutions of a class of special harmonic equations by making use of $W^{1,p}$ estimate. Keywords: global weighted $W^{1,p}$ estimates; quasilinear equations; Besov regularity