A singular perturbation limit of diffused interface energy with a fixed   contact angle condition
  We study a general asymptotic behavior of critical points of a diffused interface energy with a fixed contact angle condition defined on a domain $\Omega \subset \mathbb{R}^n$. We show that the limit varifold derived from the diffused energy satisfies a generalized contact angle condition on the boundary under a set of assumptions. 
Takashi Kagaya, Yoshihiro Tonegawa
math.AP