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

M. Goldman; M. Novaga

doi:10.1007/s00526-011-0435-6

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

M. Goldman
, M. Novaga

University of Padova

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	297-318
Number of pages	22
Journal	Calculus of Variations and Partial Differential Equations
Volume	44
Issue number	3-4
DOIs	https://doi.org/10.1007/s00526-011-0435-6
Publication status	Published - 1 Jul 2012

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AB - 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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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

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

Abstract

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