A singular perturbation problem with integral curvature bound
Preprint Series # 803
Nagase, Yuko and Tonegawa, Yoshihiro A singular perturbation problem with integral curvature bound. (2006);
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 concentrate on
one rectifiable set and has square integrable curvature.