Dept. Math, Hokkaido Univ. EPrints Server

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);

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Abstract

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.

Item Type:Preprint
Additional Information:40 Professor Yoshihiro Tonegawa
Uncontrolled Keywords:diffused interface, curvature, phase field model.
Subjects:28-xx MEASURE AND INTEGRATION
35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1615