Volume-constrained minimizers for the prescribed curvature problem in periodic media

Abstract

We establish existence of compact minimizers of the prescribed mean curvature problem with volume constraint in periodic media. As a consequence, we construct compact approximate solutions to the prescribed mean curvature equation. We also show convergence after rescaling of the volume-constrained minimizers towards a suitable Wulff Shape, when the volume tends to infinity.Comment: In this version the statement of Lemma 2.5 has been corrected with respect to the published versio