Work

Minimizing solutions of degenerate vector Allen–Cahn equations with three wells in ℝ 2

Year: 2026

Type: article

Abstract: We characterize all minimizers of the vector-valued Allen–Cahn equation in ℝ 2 under the assumption that the potential W has three wells and that the associated degenerate metric does not satisfy the usual strict triangle inequality. These minimizers depend on one variable only in a suitable coordinate system. In particular, we show that no minimizing solution to Δ u = ∇ W ( u ) on ℝ 2 can approach the three distinct values of the potential wells.

Source: Comptes Rendus Mathématique

DOI: 10.5802/crmath.818

Authors: Lia Bronsard, Étienne Sandier, Peter Sternberg

Institutions: McMaster University, Université Paris-Est Créteil, Indiana University Bloomington, Indiana University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7135193241

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Cites: 18

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