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• W2964117006 abstract "In this article, we study the second variation of the energy functional associated to the Allen–Cahn equation on closed manifolds. Extending well-known analogies between the gradient theory of phase transitions and the theory of minimal hypersurfaces, we prove the upper semicontinuity of the eigenvalues of the stability operator and consequently obtain upper bounds for the Morse index of limit interfaces which arise from solutions with bounded energy and index without assuming any multiplicity or orientability condition on these hypersurfaces. This extends some recent results of Le (Indiana Univ Math J 60:1843–1856, 2011; J Math Pures Appl 103:1317–1345, 2015)) and Hiesmayr (arXiv:1704.07738 preprint [math.DG], 2017)." @default.
• W2964117006 created "2019-07-30" @default.
• W2964117006 creator A5020959419 @default.
• W2964117006 date "2019-01-03" @default.
• W2964117006 modified "2023-09-26" @default.
• W2964117006 title "The Second Inner Variation of Energy and the Morse Index of Limit Interfaces" @default.
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• W2964117006 doi "https://doi.org/10.1007/s12220-018-00134-7" @default.
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