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

Department of Mathematical Sciences

Universidad de Valparaíso
Pontificia Universidad Católica de Chile
Institut Universitaire de France

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

15 Citations (SciVal)

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

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00229-011-0492-3

Cite this

@article{38fc270b7c06401bbe491aaaf40bb37d,

title = "Solutions of the Allen-Cahn equation which are invariant under screw-motion",

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.",

author = "\{del Pino\}, Manuel and Monica Musso and Frank Pacard",

year = "2012",

month = jul,

day = "1",

doi = "10.1007/s00229-011-0492-3",

language = "English",

volume = "138",

pages = "273--286",

journal = "Manuscripta Mathematica",

issn = "0025-2611",

publisher = "Springer New York",

number = "3-4",

}

TY - JOUR

T1 - Solutions of the Allen-Cahn equation which are invariant under screw-motion

AU - del Pino, Manuel

AU - Musso, Monica

AU - Pacard, Frank

PY - 2012/7/1

Y1 - 2012/7/1

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/84860751599

U2 - 10.1007/s00229-011-0492-3

DO - 10.1007/s00229-011-0492-3

M3 - Article

AN - SCOPUS:84860751599

SN - 0025-2611

VL - 138

SP - 273

EP - 286

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

IS - 3-4

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this