Solutions of the Allen-Cahn equation which are invariant under screw-motion

Manuel del Pino; Monica Musso; Frank Pacard

doi:10.1007/s00229-011-0492-3

Solutions of the Allen-Cahn equation which are invariant under screw-motion

Manuel del Pino
, Monica Musso
, Frank Pacard

University of Chile
Pontificia Universidad Católica de Chile
Institut Universitaire de France

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We study entire solutions of the Allen-Cahn equation which are defined in the 3-dimensional Euclidean space and which are invariant under screw-motion. In particular, we discuss the existence and non existence of nontrivial solutions whose nodal set is a helicoid of ℝ ³.

langue originale	Anglais
Pages (de - à)	273-286
Nombre de pages	14
journal	Manuscripta Mathematica
Volume	138
Numéro de publication	3-4
Les DOIs	https://doi.org/10.1007/s00229-011-0492-3
état	Publié - 1 juil. 2012

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10.1007/s00229-011-0492-3

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abstract = "We study entire solutions of the Allen-Cahn equation which are defined in the 3-dimensional Euclidean space and which are invariant under screw-motion. In particular, we discuss the existence and non existence of nontrivial solutions whose nodal set is a helicoid of ℝ 3.",

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AU - Musso, Monica

AU - Pacard, Frank

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AB - We study entire solutions of the Allen-Cahn equation which are defined in the 3-dimensional Euclidean space and which are invariant under screw-motion. In particular, we discuss the existence and non existence of nontrivial solutions whose nodal set is a helicoid of ℝ 3.

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Solutions of the Allen-Cahn equation which are invariant under screw-motion

Résumé

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