3 papers
math.AP2025
-convergence for higher order nonlocal phase transitions
Hardy Chan, Serena Dipierro, Mattia Freguglia +2
For every , we study the asymptotic behavior of the -rescaled sum of the -fractional Allen-Cahn energy and the squared -norm of its first variation…
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 \(\mathbb{R}^{n+1}\) is one-dimensional if \(n \leq 7\). A stronger vers…
math.AP2024
Spectral properties of Lévy Fokker--Planck equations
Hardy Chan, Marco A. Fontelos, María del Mar González
Hermite polynomials, which are associated to a Gaussian weight and solve the Laplace equation with a drift term of linear growth, are classical in analysis and well-understood via…