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

2019/04/16 by Changfeng Gui, Qinfeng Li, Gui, Changfeng +1
Computer Science · Mathematics · #35J15 #35J20 #35J91 #53A10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Primary 35B06

paper · pdf · doi:10.48550/arxiv.1904.07443

openalex publication_date 2019/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study stable solutions to the fractional equation (-Δ)^s u =f(u), |u| lt; 1 in ℝ^d,where 0max\0, 1-2s\. We obtain sharp energy estimates for 0

Citations

• Local and global minimizers for a variational energy involving a fractional norm
• Hitchhiker's guide to the fractional Sobolev spaces
• Nonlinear equations for fractional Laplacians I: Regularity, maximum principles, and Hamiltonian estimates

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