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

Abstract

In the present paper, we study the existence of Brakke-type weak mean curvature flow satisfying a prescribed contact angle condition for a general angle $\theta \in (0,\pi )$ via Ilmanen's regularization. The main ingredients of the result are the extension of Ilmanen's regularization to the capillarity and the derivation of the first variation estimates for the interior and wetted boundary varifolds separately.

The paper consists of 28 pages and includes 2 figures. I have corrected minor mistakes from the third version. I have also corrected the admissible class used in the minimization problem of Ilmanen's functional (this does not affect the rest part of this paper). To appear in Ann. Sc. Norm. Super. Pisa, Cl. Sci