Published Paper

Inserted: 6 mar 2024
Last Updated: 6 mar 2024

Journal: Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.
Year: 2023
Doi: 10.4171/RLM/1017

Abstract:

In this paper we study a partially overdetermined mixed boundary value problem for domains $\Omega$ contained in an unbounded set $\mathcal C$. We introduce the notion of Cheeger set relative to $\mathcal C$ and show that if a domain $\Omega \subset \mathcal C$ admits a solution of the overdetermined problem, then it coincides with its relative Cheeger set. We also study the related problem of characterizing constant mean curvature surfaces $\Gamma$ inside $\mathcal C$. In the case when $\mathcal C$ is a cylinder we obtain further results whenever the relative boundary of $\Omega$ or the surface $\Gamma$ is a graph on the base of the cylinder.