<Reference List> | |
Type: | Preprint |
National /International: | International |
Title: | Interacting free boundaries in obstacle problems |
Publication Date: | 2024-02-28 |
Authors: |
- Damião J. Araújo
- Rafayel Teymurazyan |
Abstract: | We study obstacle problems governed by two distinct types of diffusion operators, involving interacting free boundaries. We obtain a rather surprising coupling property, leading to a comprehensive analysis of the free boundary. More precisely, we show that near regular points of a coordinate function, the free boundary is analytic, whereas singular points lie on a smooth manifold. Additionally, we prove that uncoupled free boundary points are singular, indicating that regular points lie exclusively on the coupled free boundary. Furthermore, optimal regularity, non-degeneracy, and lower dimensional Hausdorff measure estimates are obtained. The sharpness of assumptions is illustrated by explicit examples. |
Institution: | DMUC 24-09 |
Online version: | http://www.mat.uc.pt...prints/eng_2024.html |
Download: | Not available |