Joaquim Serra

activity

20242026

most citedFractional Sobolev spaces on Riemannian manifolds

1 citations · 1 across the 5 of their papers we have counts for

collaborators

Showing 2025Show all

2 papers · 1 filter

math.AP2025

On stable solutions to the Allen-Cahn equation with bounded energy density in $R^{4}$

Enric Florit-Simon, Joaquim Serra

We show that stable solutions $u : R^{4} \to (- 1, 1)$ 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 $R^{n + 1}$ is one-dimensional if $n \leq 7$ . A stronger version…

On stable solutions to the Allen-Cahn equation with bounded energy density in R4

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

On stable solutions to the Allen-Cahn equation with bounded energy density in $R^{4}$