# Nondivergence elliptic and parabolic problems with irregular obstacles

## TL;DR

This paper establishes advanced regularity estimates for solutions to elliptic and parabolic obstacle problems with irregular obstacles and discontinuous coefficients, advancing the understanding of their mathematical properties.

## Contribution

It provides weighted Calderón-Zygmund estimates, Morrey regularity, and Hölder continuity results for solutions in nondivergence form with irregular obstacles.

## Key findings

- Weighted Calderón-Zygmund estimates proved
- Morrey regularity of the Hessian established
- Hölder continuity of the gradient demonstrated

## Abstract

We prove the natural weighted Calder\'{o}n and Zygmund estimates for solutions to elliptic and parabolic obstacle problems in nondivergence form with discontinuous coefficients and irregular obstacles. We also obtain Morrey regularity results for the Hessian of the solutions and H\"{o}lder continuity of the gradient of the solutions.