Thin one-phase almost minimizers. (April 2020)

• Record Type: Journal Article
• Authors: De Silva, D.; Savin, O.
• Is Part Of: Nonlinear analysis. Volume 193(2020)
• Publication Date: 2020-04
• Subjects: 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.2019.04.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider almost minimizers to the thin-one phase energy functional and we prove optimal regularity of the solution and partial regularity of the free boundary. We recover the theory for energy minimizers developed in De Silva and Roquejoffre (2012) and De Silva and Savin (2015). Our methods are based on a noninfinitesimal notion of viscosity solutions we introduced in De Silva and Savin (2018).