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

Cozzi, Matteo; Valdinoci, Enrico

doi:10.5802/jep.45

Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium
[Minimiseurs proches d’un plan pour une énergie non locale de type Ginzburg-Landau dans un milieu périodique]

Cozzi, Matteo ¹ ; Valdinoci, Enrico ²

¹ BGSMath Barcelona Graduate School of Mathematics and Departament de Matemàtiques, Universitat Politècnica de Catalunya Diagonal 647, E-08028 Barcelona (Spain)
² Weierstraß Institut für Angewandte Analysis und Stochastik Mohrenstraße 39, D-10117 Berlin (Germany) and Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Via Saldini 50, I-20133 Milano (Italy) and School of Mathematics and Statistics, University of Melbourne Grattan Street, Parkville, VIC-3010 Melbourne (Australia)

Journal de l’École polytechnique — Mathématiques, Tome 4 (2017), pp. 337-388.

Résumé
Abstract

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.

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.

Reçu le : 2016-05-30
Accepté le : 2017-02-01
Publié le : 2017-03-14

MR Zbl

DOI : 10.5802/jep.45

Classification : 35R11, 35A15, 35B08, 82B26, 35B65
Keywords: Non-local energies, phase transitions, plane-like minimizers, fractional Laplacian
Mot clés : Énergies non locales, transitions de phase, minimiseurs de type plan, laplacien fractionnaire

Affiliations des auteurs :

Cozzi, Matteo ¹ ; Valdinoci, Enrico ²

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     title = {Plane-like minimizers for {a~non-local~Ginzburg-Landau-type} energy in~a~periodic~medium},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
     pages = {337--388},
     publisher = {Ecole polytechnique},
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Cozzi, Matteo; Valdinoci, Enrico. Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium. Journal de l’École polytechnique — Mathématiques, Tome 4 (2017), pp. 337-388. doi : 10.5802/jep.45. http://www.numdam.org/articles/10.5802/jep.45/

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