Anisotropic curvature flow in a very thin domain

Abstract

The asymptotic limit of the anisotropic curvature flow in a very thin domain as its width goes to zero is studied. The problem is formulated by the level set method in the framework of the homogenization of partial differential equations. We show the existence and uniqueness of the limit anisotropic curvature flow in the limit domain, and give rigorously the effective partial differential equation which describes the motion of the flow.