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 points/local minimizers of elliptic energies interacting with a confinement potential. Second, we prove an Alexandrov-type theorem for crystalline isoperimetric problems.
CITATION STYLE
Delgadino, M. G., Maggi, F., Mihaila, C., & Neumayer, R. (2018). Bubbling with L 2-Almost Constant Mean Curvature and an Alexandrov-Type Theorem for Crystals. Archive for Rational Mechanics and Analysis, 230(3), 1131–1177. https://doi.org/10.1007/s00205-018-1267-8
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