Regularity of the free boundary for a Bernoulli-type parabolic problem with variable coefficients. (November 2016)

• Record Type: Journal Article
• Authors: Backing, Thomas
• Is Part Of: Nonlinear analysis. Volume 146(2016)
• Page Start: 74
• Page End: 99
• Publication Date: 2016-11
• Subjects: Free boundary problems -- Singular perturbation; 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.2016.08.013
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this work the regularity of the free boundary for a class of parabolic free boundary problems with variable coefficients is studied. Under the main hypothesis that the free boundary is Lipschitz, the main result is that the free boundary is in fact C 1, α surfaces, thereby implying that the viscosity solution is in fact classical in this case.