# Asymptotically regular operators in generalized Morrey spaces

## TL;DR

This paper establishes Calderón-Zygmund estimates for nonlinear p-Laplacian type equations in generalized Morrey spaces, leading to insights on asymptotic regularity and generalized Hölder regularity of solutions under minimal assumptions.

## Contribution

It introduces Calderón-Zygmund estimates for nonlinear operators in generalized Morrey spaces and explores asymptotic regularity with minimal regularity assumptions.

## Key findings

- Calderón-Zygmund estimates for p-Laplacian type equations in generalized Morrey spaces.
- Asymptotic regularity of nonlinear operators under minimal assumptions.
- Generalized Hölder regularity of solutions with minimal weight function restrictions.

## Abstract

We obtain Calder\'on-Zygmund type estimates in generalized Morrey spaces for nonlinear equations of $p$-Laplacian type. Our result is obtained under minimal regularity assumptions both on the operator and on the domain. This result allows us to study asymptotically regular operators. As a byproduct, we obtain also generalized H\"older regularity of the solutions under some minimal restrictions of the weight functions.