Electron. J. Diff. Equ., Vol. 2016 (2016), No. 119, pp. 1-12.

Multiplicity of critical points for the fractional Allen-Cahn energy

Dayana Pagliardini

In this article we study the fractional analogue of the Allen-Cahn energy in bounded domains. We show that it admits a number of critical points which approaches infinity as the perturbation parameter tends to zero.

Submitted March 4, 2016. Published May 13, 2016.
Math Subject Classifications: 35R11, 58J37.
Key Words: Allen-Cahn energy; fractional PDE; critical point, genus.

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Dayana Pagliardini
Scuola Normale Superiore
Piazza dei Cavalieri 7
56126 Pisa, Italy
email: dayana.pagliardini@sns.it

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