Homogenization and error estimates of free boundary velocities in periodic media

Abstract

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-Linéaire 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.

Keywords:

• nonlinear PDEs
• homogenization
• free boundary problems

AMS Subject Classifications::

• 35R35
• 35B27