Bent rectangles as viscosity solutions over a circle. (September 2015)

• Record Type: Journal Article
• Authors: Giga, Yoshikazu; Górka, Przemysław; Rybka, Piotr
• Is Part Of: Nonlinear analysis. Volume 125(2015)
• Page Start: 518
• Page End: 549
• Publication Date: 2015-09
• Subjects: primary 53C44 -- secondary 35K55 35D40 35B51; Singular energies -- Driven curvature flow -- Viscosity solutions -- Comparison principle; 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.2015.05.033
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the motion of the so-called bent rectangles by the singular weighted mean curvature. We are interested in the curves which can be rendered as graphs over a smooth one-dimensional reference manifold. We establish a sufficient condition for that. Once we deal with graphs we can have the tools of the viscosity theory available, like the Comparison Principle. With its help we establish uniqueness of variational solutions constructed by the authors (Giga et al., 2013). In addition, we establish a criterion for the mobility coefficient guaranteeing vertex preservation.