On Gradient Flows with Obstacles and Euler's Elastica
arXiv:1903.00429
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.
50 pages, 1 figure