On the fine structure of the solutions to nonlinear thin two-membrane problems in 2D
Analysis of PDEs
2024-05-10 v1
Abstract
We prove a structure theorem for the solutions of nonlinear thin two-membrane problems in dimension two. Using the theory of quasi-conformal maps, we show that the difference of the sheets is topologically equivalent to a solution of the linear thin obstacle problem, thus inheriting its free boundary structure. More precisely, we show that even in the nonlinear case the branching points can only occur in finite number. We apply our methods to one-phase free boundaries approaching a fixed analytic boundary and to the solutions of a one-sided two-phase Bernoulli problem.
Keywords
Cite
@article{arxiv.2405.05799,
title = {On the fine structure of the solutions to nonlinear thin two-membrane problems in 2D},
author = {Lorenzo Ferreri and Luca Spolaor and Bozhidar Velichkov},
journal= {arXiv preprint arXiv:2405.05799},
year = {2024}
}