Homogenization and Phase Separation with Fixed Wells—The Supercritical Case

SIAM Journal on Mathematical Analysis, vol. 57, pp. 2138–2173

Abstract

Abstract. A variational model for the interaction between homogenization and phase separation is considered in the regime where the former happens at a finer scale than the latter. The first order [Formula: see text]-limit is proven to exhibit a separation of scales which has been previously conjectured in [A. Braides and C. I. Zeppieri, Interfaces Free Bound., 11 (2009), pp. 61–118; A. Hagerty, A Note on Homogenization Effects on Phase Transition Problems, arXiv:1811.07357, 2018].

Authors 3

1. Riccardo Cristoferi

   Radboud University Nijmegen

   Affiliation as printed

   Department of Mathematics - IMAPP, Radboud University, Heyendaalseweg, 6525 AJ Nijmegen, The Netherlands

2. Irene Fonseca

   Carnegie Mellon University

   Affiliation as printed

   Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213-3890 USA

3. Likhit Ganedi Aachen Institut für Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Mathematik, RWTH Aachen, Templergraben, 52062 Aachen, Germany