On the second inner variations of Allen-Cahn type energies and applications to local minimizers

DOI10.1016/j.matpur.2014.10.014zbMath1405.49008arXiv1408.6481OpenAlexW2964180324MaRDI QIDQ2344549

Nam Q. Le

Publication date: 15 May 2015

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.6481

zbMATH Keywords

second variationPoincaré inequalitylocal minimizerAllen-Cahn functionalvolume constrained area-minimizing surface

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Methods involving semicontinuity and convergence; relaxation (49J45) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items (6)

On upper semicontinuity of the Allen–Cahn twisted eigenvalues ⋮ Instability of solutions to the Ginzburg-Landau equation on \(S^n\) and \(\mathbb{C} \mathbb{P}^n\) ⋮ Spectrum and index of two-sided Allen–Cahn minimal hypersurfaces ⋮ Regularity of minimal and CMC stable hypersurfaces: a brief overview ⋮ The second inner variation of energy and the Morse index of limit interfaces ⋮ Asymptotic behavior of Allen-Cahn-type energies and Neumann eigenvalues via inner variations

Cites Work

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• On the first and second variations of a nonlocal isoperimetric problem
• Variational convergence for functionals of Ginzburg-Landau type
• Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions

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