Minimizers of a free boundary problem on three-dimensional cones. (January 2023)

• Record Type: Journal Article
• Authors: Allen, Mark; Barker, Blake; Gardiner, Jason; Zhao, Mingyan
• Is Part Of: Nonlinear analysis. Volume 226(2023)
• Publication Date: 2023-01
• Subjects: 35R35 -- 35R01 -- 35J20 -- 65M99; Free boundary problem -- One-phase problem -- Computer assisted proof -- Interval arithmetic; 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.2022.113152
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a free boundary problem on three-dimensional cones depending on a parameter c and study when the free boundary is allowed to pass through the vertex of the cone. Combining analysis and computer-assisted proof, we show that when c ≤ 0 . 43 the free boundary may pass through the vertex of the cone.