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

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 :
Accepté le :
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DOI : https://doi.org/10.5802/jep.45
Classification : 35R11,  35A15,  35B08,  82B26,  35B65
Mots clés : Énergies non locales, transitions de phase, minimiseurs de type plan, laplacien fractionnaire
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     author = {Cozzi, Matteo and Valdinoci, Enrico},
     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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     year = {2017},
     doi = {10.5802/jep.45},
     zbl = {06754330},
     mrnumber = {3623357},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jep.45/}
}
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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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