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

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.