Global minimizers of the Allen-Cahn equation in dimension \(n\geq 8\)

DOI10.1016/j.matpur.2017.05.006zbMath1380.35071arXiv1606.05315OpenAlexW2963085578MaRDI QIDQ1679730

Kelei Wang, Yong Liu, Wei, Juncheng

Publication date: 22 November 2017

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.05315

zbMATH Keywords

Allen-Cahn equationglobal minimizerDe Giorgi conjectureminimal cones

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61)

Related Items (14)

Half-space theorems for the Allen-Cahn equation and related problems ⋮ On De Giorgi's conjecture: recent progress and open problems ⋮ Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane ⋮ Saddle-shaped solutions for the fractional Allen-Cahn equation ⋮ On the existence of \(N\)-junctions for a symmetric nonnegative potential with \(N+1\) zeros ⋮ On the triple junction problem without symmetry hypotheses ⋮ Unnamed Item ⋮ Allen-Cahn min-max on surfaces ⋮ Long-range Phase Coexistence Models: Recent Progress on the Fractional Allen-Cahn Equation ⋮ On a free boundary problem and minimal surfaces ⋮ Uniqueness and stability of the saddle-shaped solution to the fractional Allen-Cahn equation ⋮ Energy minimality property of the connecting solution of the Painlevé phase transition model ⋮ Simons cone and saddle solutions of the Allen-Cahn equation ⋮ The geometric structure of interfaces and free boundaries

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