A Serrin-type problem with partial knowledge of the domain. (July 2021)

• Record Type: Journal Article
• Authors: Dipierro, Serena; Poggesi, Giorgio; Valdinoci, Enrico
• Is Part Of: Nonlinear analysis. Volume 208(2021)
• Publication Date: 2021-07
• Subjects: primary 35N25 53A10 35B35 -- secondary 35A23; Serrin's overdetermined problem -- Torsional rigidity -- Integral identities -- Stability -- Quantitative estimates; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112330
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We present a quantitative estimate for the radially symmetric configuration concerning a Serrin-type overdetermined problem for the torsional rigidity in a bounded domain Ω ⊂ R N, when the equation is known on Ω ∖ ω ¯ only, for some open subset ω ⋐ Ω . The problem has concrete motivations in optimal heating with malfunctioning, laminar flows and beams with small inhomogeneities.