Quantitative stability estimates for a two-phase Serrin-type overdetermined problem. (September 2022)

• Record Type: Journal Article
• Authors: Cavallina, Lorenzo; Poggesi, Giorgio; Yachimura, Toshiaki
• Is Part Of: Nonlinear analysis. Volume 222(2022)
• Publication Date: 2022-09
• Subjects: 35B35 -- 35J15 -- 35N25 -- 35Q93; Two-phase -- Overdetermined problem -- Serrin's problem -- Transmission condition -- Stability; 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.2022.112919
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we deal with an overdetermined problem of Serrin-type with respect to a two-phase elliptic operator in divergence form with piecewise constant coefficients. In particular, we consider the case where the two-phase overdetermined problem is close to the one-phase setting. First, we show quantitative stability estimates for the two-phase problem via a one-phase stability result. Furthermore, we prove non-existence for the corresponding inner problem by the aforementioned two-phase stability result.