On gradient flows with obstacles and Euler's elastica. (March 2020)

• Record Type: Journal Article
• Authors: Müller, Marius
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: primary 35K87 35R35 -- secondary 49J40 34G20; Gradient flows in metric spaces -- Higher order PDE's -- Elastic bending energy; 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.2019.111676
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We examine a steepest energy descent flow with obstacle constraint in higher order energy frameworks where the maximum principle is not available. We construct the flow under general assumptions using De Giorgi's minimizing movement scheme. Our main application will be the elastic flow of graph curves with Navier boundary conditions for which we study long-time existence and asymptotic behavior.