Overdetermined problems and relative Cheeger sets in unbounded domains

2022/03/16 by Afonso, Danilo Gregorin, Iacopetti, Alessandro, Pacella, Filomena · 2 citations
#35J25 #35N25 #49Q10 #53A10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.08940

Abstract

In this paper we study a partially overdetermined mixed boundary value problem for domains Ω contained in an unbounded set \mathcal C. We introduce the notion of Cheeger set relative to \mathcal C and show that if a domain Ω⊂ \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 Γ inside \mathcal C. In the case when \mathcal C is a cylinder we obtain further results whenever the relative boundary of Ω or the surface Γ is a graph on the base of the cylinder.

Cited by

• Bifurcating domains for an overdetermined eigenvalue problem in cylinders
• Spectral minimal partitions of unbounded domains

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