Low Complexity Solutions of the Allen–Cahn Equation on Three-spheres

Haslhofer, Robert ; Ivaki, Mohammad N.

Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 287-291

Résumé

In this short note, we prove that on the three-sphere with any bumpy metric there exist at least two pairs of solutions of the Allen–Cahn equation with spherical interface and index at most two. The proof combines several recent results from the literature.

Détail

DOI : 10.4153/CMB-2018-033-4

Mots-clés : Allen–Cahn equation, phase transition, small index

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