Semantic Scholar Open Access 2017 45 sitasi

The Second Inner Variation of Energy and the Morse Index of Limit Interfaces

P. Gaspar

Abstrak

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).

Topik & Kata Kunci

Mathematics

Penulis (1)

P. Gaspar

Format Sitasi

APA MLA BibTeX

Gaspar, P. (2017). The Second Inner Variation of Energy and the Morse Index of Limit Interfaces. https://doi.org/10.1007/s12220-018-00134-7

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Informasi Jurnal

Tahun Terbit: 2017
Bahasa: en
Total Sitasi: 45×
Sumber Database: Semantic Scholar
DOI: 10.1007/s12220-018-00134-7
Akses: Open Access ✓