Long-range phase coexistence models: recent progress on the fractional Allen-Cahn equation

2018/03/10 by Serena Dipierro, Enrico Valdinoci, Dipierro, Serena +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1803.03850

openalex publication_date 2018/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this set of notes, we present some recent developments on the fractional Allen-Cahn equation (-Δ)^s u = u-u³, with special attention to Γ-convergence results, energy and density estimates, convergence of level sets, Hamiltonian estimates, rigidity and symmetry results.

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• Some Energy Estimates for Stable Solutions to Fractional Allen-Cahn Equations
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