A dynamical approach to the variational inequality on modified elastic graphs
Shinya Okabe, Kensuke Yoshizawa · Geometric Flows · 2020
Abstract We consider the variational inequality on modified elastic graphs. Since the variational inequality is derived from the minimization problem for the modified elastic energy defined on graphs with the unilateral constraint, a solution to the variational inequality can be constructed by the direct method of calculus of variations. In this paper we prove the existence of solutions to the variational inequality via a dynamical approach. More precisely, we construct an L 2 -type gradient flow corresponding to the variational inequality and prove the existence of solutions to the variational inequality via the study on the limit of the flow.