We consider a singular perturbation problem of Modica-Mortola functional as the thickness of diffused interface approaches to zero. We assume that sequence of functions have uniform energy and square-integral curvature bounds in two dimension. We show that the limit measure concentrates on one rectifiable set and has square integrable curvature.
"A singular perturbation problem with integral curvature bound." Hiroshima Math. J. 37 (3) 455 - 489, November 2007. https://doi.org/10.32917/hmj/1200529813