Gamma-convergence results for phase-field approximations of the 2D-Euler Elastica Functional
Max Planck Institute for Mathematics in the
Received: 25 November 2010
Revised: 26 January 2012
We establish some new results about the Γ-limit, with respect to the L1-topology, of two different (but related) phase-field approximations 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 ℰε, and show that in general the Γ-limits of ℰε and do not coincide on indicator functions of sets with non-smooth boundary. More precisely we show that the domain of the Γ-limit of strictly contains the domain of the Γ-limit of ℰε.
Mathematics Subject Classification: 49J45 / 34K26 / 49Q15 / 49Q20
Key words: Γ-convergence / relaxation / singular perturbation / geometric measure theory
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