Work

Stable solutions of the Allen--Cahn equation in dimension three are one-dimensional

Year: 2026

Type: preprint

Abstract: We prove that every bounded stable solution of the Allen--Cahn equation in $\mathbb R^3$ is one-dimensional. As a consequence, this shows the validity of De Giorgi's conjecture for monotone solutions in dimension four.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.30194

Authors: Chan, Hardy, Fernández-Real, Xavier, Figalli, Alessio, Florit-Simon, Enric, Serra, Joaquim

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214291465

Cites:

Cited by: 1

Related to: 10