Bubbling with L 2-Almost Constant Mean Curvature and an Alexandrov-Type Theorem for Crystals

Matias G. Delgadino, Francesco Maggi*, Cornelia Mihaila, Robin Neumayer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1131-1177
Number of pages47
JournalArchive for Rational Mechanics and Analysis
Volume230
Issue number3
DOIs
StatePublished - Dec 1 2018

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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