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We consider a non-local phase transition equation set in a periodic medium and we construct solutions whose interface stays in a slab of prescribed direction and universal width. The solutions constructed also enjoy a local minimality property with respect to a suitable non-local energy functional.

Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium / M. Cozzi, E. Valdinoci. - In: JOURNAL DE L'ÉCOLE POLYTECHNIQUE. MATHÉMATIQUES. - ISSN 2429-7100. - 4:(2017), pp. 337-388. [10.5802/jep.45]

Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium

M. Cozzi;E. Valdinoci
2017

Abstract

We consider a non-local phase transition equation set in a periodic medium and we construct solutions whose interface stays in a slab of prescribed direction and universal width. The solutions constructed also enjoy a local minimality property with respect to a suitable non-local energy functional.
Nous considérons une équation de transition de phase non locale dans un milieu périodique et nous construisons des solutions dont l’interface se trouve dans un domaine de direction prescrite et de largeur universelle. Les solutions construites jouissent aussi d’une propriété de minimalité locale par rapport à une certaine fonctionnelle d’énergie non locale.
Fractional Laplacian; Non-local energies; Phase transitions; Plane-like minimizers
Settore MAT/05 - Analisi Matematica
Settore MATH-03/A - Analisi matematica
2017
Article (author)
01 - Articolo su periodico
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/734215
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