We establish some new results about the Γ-limit, with respect to the L1-topology, of two different (but related) phase-field approximations $\{{ℰ}_{\}},\{{\widetilde{ℰ}}_{\}}$ ℰ ε ε ,   x10ff65; ℰ ε ε of the so-called Euler’s Elastica Bending Energy for curves in the plane. In particular we characterize theΓ-limit as ε → 0 of ℰε, and show that in general the Γ-limits of ℰεand $\widetilde{ℰ}$ x10ff65; ℰ ε do not coincide on indicator functions of sets with non-smooth boundary. More precisely we show that the domain of theΓ-limit of $\widetilde{ℰ}$ x10ff65;...