Calculus of Variations and Geometric Measure Theory

A. Garroni - B. Niethammer

Correctors and error estimates in the homogenization of a Mullins-Sekerka problem

created on 04 Jan 2002
modified on 26 Oct 2002


Published Paper

Inserted: 4 jan 2002
Last Updated: 26 oct 2002

Journal: Ann. Inst. H. Poincare` Anal. Nonlineaire
Volume: 19
Number: 4
Pages: 371-393
Year: 2002


We study the homogenization of a Mullins-Sekerka free boundary problem which serves as a model for coarsening of nuclei in a first order phase transformation. We consider a regime where the volume fraction of the nuclei is small but screening effects are not negligible. The limit equation was recently derived in Niethammer and Otto. We improve this convergence result by constructing correctors and providing error estimates in terms of the volume fraction. This yields in particular an asymptotic expansion for the growth rate of the nuclei.

Keywords: Homogenization, Mullins-Sekerka problem , domain coarsening, correctors