Calculus of Variations and Geometric Measure Theory
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M. Delgadino - F. Maggi - C. Mihaila - R. Neumayer

Bubbling with $L^2$-almost constant mean curvature and an Alexandrov-type theorem for crystals

created by maggi on 29 May 2017
modified on 13 Jul 2020


Published Paper

Inserted: 29 may 2017
Last Updated: 13 jul 2020

Journal: Archive for Rational Mechanics and Analysis
Year: 2017


A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measured in an integral rather than in a uniform sense. Two main applications of the compactness theorem are discussed. First, we obtain a description of critical pointslocal minimizers of elliptic energies interacting with a confinement potential. Second, we prove an Alexandrov-type theorem for crystalline isoperimetric problems.


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