On the second inner variation of the Allen-Cahn functional and its applications

DOI10.1512/IUMJ.2011.60.4505zbMath1273.49017arXiv1009.5649OpenAlexW2962936276MaRDI QIDQ4905820

Nam Q. Le

Publication date: 21 February 2013

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.5649

zbMATH Keywords

stabilitysecond variationMorse indexAllen-Cahn functional

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Methods involving semicontinuity and convergence; relaxation (49J45) Variational principles of physics (49S05)

Related Items (8)

On upper semicontinuity of the Allen–Cahn twisted eigenvalues ⋮ Tightness for a stochastic Allen-Cahn equation ⋮ Nondegeneracy and stability in the limit of a one-phase singular perturbation problem ⋮ 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 ⋮ On the second inner variations of Allen-Cahn type energies and applications to local minimizers

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