2 papers
math.AP2025
On stable solutions to the Allen-Cahn equation with bounded energy density in
Enric Florit-Simon, Joaquim Serra
We show that stable solutions to the Allen-Cahn equation with bounded energy density (or equivalently, with cubic energy growth) are one-dimensional. Thi…
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…