A diffused interface whose chemical potential lies in a Sobolev space

Yoshihiro Tonegawa
2009 Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V  
We study a singular perturbation problem arising in the scalar twophase field model. Given a sequence of functions with a uniform bound on the surface energy, assume the Sobolev norms W 1, p of the associated chemical potential fields are bounded uniformly, where p > n 2 and n is the dimension of the domain. We show that the limit interface as ε tends to zero is an integral varifold with a sharp integrability condition on the mean curvature.
doi:10.2422/2036-2145.2005.3.05 fatcat:gu5m5r5tajatbnvhp4izyl6cim