# A note on gradient estimates for p-Laplacian equations

## TL;DR

This paper improves gradient estimate methods for p-Laplacian equations by relaxing assumptions, utilizing nonlinear potential theory and compactness results to analyze weak solutions.

## Contribution

It demonstrates that certain assumptions can be dropped when seeking weak solutions, enhancing the theoretical framework for p-Laplacian equations.

## Key findings

- Relaxation of assumptions in gradient estimates
- Use of nonlinear potential theory for $L^ty$ estimates
- Application of Riesz-Fre9chet-Kolmogorov theorem for compactness

## Abstract

The aim of this short paper is to show that some assumptions in [10] can be relaxed and even dropped when looking for weak solutions instead of strong ones. This improvement is a consequence of two results concerning gradient terms: an $L^\infty$ estimate, which exploits nonlinear potential theory, and a compactness result, based on the classical Riesz-Fr\'echet-Kolmogorov theorem.