English

On the multiple membranes problem

Analysis of PDEs 2018-01-18 v1

Abstract

We establish the optimal regularity for solutions to the multiple membranes problem, and perform a blow-up analysis at points on the free boundary with the highest multiplicity. This leads to a complete classification of blow-up profiles in the plane. The main technical tool is a Weiss-type monotonicity formula.

Keywords

Cite

@article{arxiv.1801.05523,
  title  = {On the multiple membranes problem},
  author = {Ovidiu Savin and Hui Yu},
  journal= {arXiv preprint arXiv:1801.05523},
  year   = {2018}
}

Comments

17 pages

R2 v1 2026-06-22T23:47:26.054Z