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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	273-286
Number of pages	14
Journal	Manuscripta Mathematica
Volume	138
Issue number	3-4
DOIs	https://doi.org/10.1007/s00229-011-0492-3
Publication status	Published - 1 Jul 2012

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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 - 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

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