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

TL;DR

This paper proves new gamma-convergence results for phase-field models approximating Euler's Elastica energy, enhancing understanding of their mathematical behavior in 2D curve modeling.

Contribution

It establishes novel gamma-convergence results for two related phase-field approximations of Euler's Elastica energy in the plane.

Findings

New gamma-limit results for phase-field approximations

Enhanced understanding of phase-field models for Euler's Elastica

Mathematical validation of approximation methods

Abstract

We establish some new results about the $\Gamma$-limit, with respect to the $L^1$-topology, of two different (but related) phase-field approximations of the so-called Euler's Elastica Bending Energy for curves in the plane.