Free boundary regularity in the multiple membrane problem in the plane

TL;DR

This paper investigates the smoothness and structure of free boundaries in a two-dimensional multiple elastic membrane problem, establishing uniqueness of blow-ups and regularity of free boundaries near intersection points.

Contribution

It proves the uniqueness of blow-ups and shows that free boundaries are $C^{1, ext{log}}$-curves near regular intersection points in the plane.

Findings

Uniqueness of blow-ups in the problem.

Free boundaries are $C^{1, ext{log}}$-curves near regular intersection points.

Enhanced understanding of free boundary regularity in elastic membranes.

Abstract

We study the regularity of free boundaries in the multiple elastic membrane problem in the plane. We prove the uniqueness of blow-ups, and that the free boundaries are $C^{1,\log}$-curves near a regular intersection point.