# Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem

## TL;DR

This paper proves that for the lower dimensional obstacle problem, the blow-up limit at generic free-boundary points is unique, resolving an open question in the mathematical analysis of such problems.

## Contribution

It establishes the almost everywhere uniqueness of blow-up limits for minimizers in the lower dimensional obstacle problem, advancing understanding of free-boundary regularity.

## Key findings

- Blow-up limits are unique at generic free-boundary points.
- Addresses an open problem from previous research.
- Enhances the theoretical framework of obstacle problems.

## Abstract

We answer a question left open in [Arch. Rat. Mech. Anal. 230 (1) (2018), 125-184] and [Arch. Rat. Mech. Anal. 230 (2) (2018), 783-784], by proving that the blow-up limit of minimizers $u$ of the lower dimensional obstacle problem is unique at generic point of the free-boundary.