# Gradient estimates for nonlinear elliptic equations with first order terms

## TL;DR

This paper investigates the existence and Lorentz regularity of solutions to nonlinear elliptic equations with first order convection or drift terms, using pointwise rearrangement estimates to handle the non-coercive nature.

## Contribution

It introduces new pointwise rearrangement estimates to analyze solutions of elliptic equations with first order terms, addressing non-coercivity issues.

## Key findings

- Established existence of solutions under new conditions.
- Derived Lorentz regularity estimates for solutions and their gradients.
- Provided pointwise estimates for rearrangements of solutions.

## Abstract

We study existence and Lorentz regularity of distributional solutions to elliptic equations with either a convection or a drift first order term. The presence of such a term makes the problem not coercive. The main tools are pointwise estimates of the rearrangements of both the solution and its gradient.