In this paper, we study a partially overdetermined mixed boundary value problem for domains Ω contained in an unbounded set C. We introduce the notion of the Cheeger set relative to C and show that if a domain Ω⊂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 C. In the case when 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.
Overdetermined problems and relative Cheeger sets in unbounded domains / Afonso, Danilo Gregorin; Iacopetti, Alessandro; Pacella, Filomena. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 34:2(2023). [10.4171/RLM/1017]
Overdetermined problems and relative Cheeger sets in unbounded domains
Afonso, Danilo Gregorin;Iacopetti, Alessandro;Pacella, Filomena
2023
Abstract
In this paper, we study a partially overdetermined mixed boundary value problem for domains Ω contained in an unbounded set C. We introduce the notion of the Cheeger set relative to C and show that if a domain Ω⊂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 C. In the case when 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.File | Dimensione | Formato | |
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