Multiple end solutions to the Allen-Cahn equation in \(\mathbb{R}^2\)
type: Item
instance of: scholarly article
title: Multiple end solutions to the Allen-Cahn equation in \(\mathbb{R}^2\)
zbMATH Open document ID: 1485.35128
author: Yong Liu
author: Michal Kowalczyk
author: Frank Pacard
published in: Séminaire Laurent Schwartz. EDP et Applications
publication date: 2022-01-17T00:00:00Z
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35B08
zbMATH DE Number: 7458094
zbMATH Keywords: Allen-Cahn equation
zbMATH Keywords: \(2k\) end solutions
MaRDI profile type: Publication
full work available at URL: slsedp.55
OpenAlex ID: W2915053687
cites work: Saddle-type solutions for a class of semilinear elliptic equations
cites work: Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
cites work: The Liouville property and a conjecture of De Giorgi.
cites work: One-dimensional symmetry of bounded entire solutions of some elliptic equations
cites work: Stable and finite Morse index solutions on 𝐑ⁿ or on bounded domains with small diffusion
cites work: Saddle solutions of the bistable diffusion equation
cites work: Moduli space theory for the Allen-Cahn equation in the plane
cites work: Multiple-end solutions to the Allen-Cahn equation in \(\mathbb R^2\)
cites work: On De Giorgi's conjecture in dimension \(N\geq 9\)
cites work: Symmetry for solutions of semilinear elliptic equations in \(\mathbb R^ N\) and related conjectures.
cites work: On complete minimal surfaces with finite Morse index in three manifolds
cites work: On a conjecture of De Giorgi and some related problems
cites work: Hamiltonian identities for elliptic partial differential equations
cites work: Symmetry of some entire solutions to the Allen-Cahn equation in two dimensions
cites work: Embedded minimal surfaces derived from Scherk's examples
cites work: The solution to a generalized Toda lattice and representation theory
cites work: Nondegeneracy of the saddle solution of the Allen-Cahn equation
cites work: The classification of four-end solutions to the Allen-Cahn equation on the plane
cites work: The space of 4-ended solutions to the Allen-Cahn equation in the plane
cites work: The moduli space of complete embedded constant mean curvature surfaces
cites work: Gluing and moduli for noncompact geometric problems
cites work: Moduli Spaces of Singular Yamabe Metrics
cites work: Minimal surfaces with the area growth of two planes: The case of infinite symmetry
cites work: Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
cites work: Q4039835
cites work: Stable solutions of the Allen-Cahn equation in dimension 8 and minimal cones
cites work: The classification of singly periodic minimal surfaces with genus zero and Scherk-type ends
cites work: Regularity of flat level sets in phase transitions
cites work: On the stability of the saddle solution of Allen–Cahn's equation
DOI: 10.5802/SLSEDP.55
description: scientific article; zbMATH DE number 7458094