Gamma-convergence results for phase-field approximations of the 2D-Euler Elastica Functional

Abstract

We establish some new results about the Γ-limit, with respect to the L1-topology, of two different (but related) phase-field approximations hbox mathcal Eε, Eε of the so-called Euler's Elastica Bending Energy for curves in the plane. In particular we characterize the Γ-limit as ε → 0 of â" °ε, and show that in general the Γ-limits of â"°ε and Eε do not coincide on indicator functions of sets with non-smooth boundary. More precisely we show that the domain of the Γ-limit of Eε strictly contains the domain of the Γ-limit of â"°ε. © EDP Sciences, SMAI, 2013.