Existence of weak mean curvature flow with prescribed contact angle via elliptic regularization

TL;DR

This paper proves the existence of weak mean curvature flows with prescribed contact angles using elliptic regularization, extending Ilmanen's method to capillarity problems for general angles.

Contribution

It establishes a compactness theorem for varifolds with contact angles and extends Ilmanen's regularization to capillarity, enabling existence results for a broad range of contact angles.

Findings

Existence of Brakke-type weak mean curvature flow with contact angle.

Extension of Ilmanen's regularization to capillarity problems.

Compactness theorem for varifolds with prescribed contact angles.

Abstract

In the present paper, we study the existence of Brakke-type weak mean curvature flow satisfying the contact angle condition for general angle $ \theta \in ( 0 , \pi ) $ via Ilmanen's regularization. The main ingredients of the result are the establishment of a compactness theorem for varifolds with the contact angle and the extension of Ilmanen's regularization to the capillarity.