# Regularizing effect of the lower-order terms in elliptic problems with Orlicz growth

## TL;DR

This paper investigates how lower-order terms influence gradient estimates in nonlinear elliptic equations with Orlicz growth, revealing their regularizing effects under various data conditions.

## Contribution

It provides new insights into the regularization effects of lower-order terms in elliptic equations with Orlicz growth, especially when data are in Lorentz/Morrey spaces.

## Key findings

- Lower-order terms can improve gradient regularity of solutions.
- Growth conditions of lower-order terms modulate regularization effects.
- Results apply to data outside the dual of the natural energy space.

## Abstract

Under various conditions on the data we analyse how appearence of lower order terms affects the gradient estimates on solutions to a general nonlinear elliptic equation of the form \[-{\rm div}\, a(x,Du)+b(x,u)=\mu\] with data $\mu$ not belonging to the dual of the natural energy space but to Lorentz/Morrey-type spaces. The growth of the leading part of the operator is governed by a function of Orlicz-type, whereas the lower-order term satisfies the sign condition and is minorized with some convex function, whose speed of growth modulates the regularization of the solutions.