Homogenization and error estimates of free boundary velocities in periodic media

摘要

In this note we describe a recent result [I.C. Kim, Homogenization of a model problem on contact angle dynamics, Comm. Partial Diff. Eqns. 33(7-9), (2008), pp. 1235-1271; I.C. Kim, Error estimates on homogenization of free boundary velocities in periodic media, Ann. Inst. H. Poincar, Anal. Non-Lineaire 26(3) (2009), pp. 99-1019] on homogenization and error estimates of a free boundary problem, which describes quasi-static contact angle dynamics on inhomogeneous surface. The method presented here also applies to more general class of free boundary problems with oscillating boundary velocities.