A singular perturbation limit of diffused interface energy with a fixed contact angle condition

Abstract

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.

11 pages

References in corpus (1)

• A fixed contact angle condition for varifolds

Cited by in corpus (4)

• Convergence of the Allen-Cahn equation with a zero Neumann boundary condition on non-convex domains
• On the concentration for a singularly perturbed problem with nonlinear Neumann boundary condition
• A fixed contact angle condition for varifolds
• Convergence of the Allen-Cahn equation with a nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle close to $90$°