Hardy Chan

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20242026

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3 papers · 1 filter

math.AP2025

$Γ$ -convergence for higher order nonlocal phase transitions

Hardy Chan, Serena Dipierro, Mattia Freguglia +2

For every $0 < s < 3/4$ , we study the asymptotic behavior of the $ε$ -rescaled sum of the $s$ -fractional Allen-Cahn energy and the squared $L^{2}$ -norm of its first variation…

math.AP2025

Convergence of the fractional Yamabe flow for arbitrary initial energy

Jingeon An-Lacroix, Hardy Chan, Pak Tung Ho

Since the seminal paper of Graham and Zworski (Invent. Math. 2003), conformal geometric problems are studied in the fractional setting. We consider the convergence of fractional Ya…

math.AP2025

Global Stable Solutions to the Free Boundary Allen--Cahn and Bernoulli Problems in 3D are One-Dimensional

Hardy Chan, Xavier Fernández-Real, Alessio Figalli +1

A long-standing conjecture of De Giorgi asserts that every monotone solution of the Allen--Cahn equation in $R^{n + 1}$ is one-dimensional if $n \leq 7$ . A stronger version…

Γ-convergence for higher order nonlocal phase transitions

Convergence of the fractional Yamabe flow for arbitrary initial energy

Global Stable Solutions to the Free Boundary Allen--Cahn and Bernoulli Problems in 3D are One-Dimensional

$Γ$ -convergence for higher order nonlocal phase transitions