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

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

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.

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