# Quantitative Homogenization for the Obstacle Problem and Its Free Boundary

## TL;DR

This paper proves quantitative homogenization for the obstacle problem and derives regularity results for the solution and free boundary.

## Contribution

The novel contribution is proving quantitative homogenization for the obstacle problem with bounded measurable coefficients.

## Key findings

- Quantitative homogenization results are established for the obstacle problem.
- Large-scale regularity is shown for both the solution and the free boundary in heterogeneous settings.

## Abstract

In this manuscript we prove quantitative homogenization results for the obstacle problem with bounded measurable coefficients. As a consequence, large-scale regularity results both for the solution and the free boundary for the heterogeneous obstacle problem are derived.