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

TL;DR

This paper investigates the asymptotic behavior of critical points in diffused interface energies with fixed contact angles, showing that their limits satisfy a generalized contact angle condition on the boundary.

Contribution

It establishes the limit behavior of diffused interface energies with fixed contact angles, connecting critical points to boundary conditions in the limit.

Findings

Limit varifold satisfies a generalized contact angle condition.

Asymptotic analysis links diffused energy critical points to boundary conditions.

Provides theoretical foundation for interface energy models with contact angles.

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.