Enric Florit-Simon

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math.AP2026

Finite index solutions to the Bernoulli problem in three dimensions are axially symmetric

Xavier FernÃ¡ndez-Real, Enric Florit-Simon, Joaquim Serra

We show that every entire solution to the Bernoulli (or one-phase) free boundary problem with finite Morse index in $R^{3}$ is axially symmetric. In fact, we additionally pr…

math.AP2026

Phase transitions with bounded index: Parallels to De Giorgi's conjecture

Enric Florit-Simon

A well-known conjecture of De Giorgi -- motivated by analogy with the Bernstein problem for minimal surfaces -- asserts the rigidity of monotone solutions to the Allen--Cahn equati…

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

Fractional Sobolev spaces on Riemannian manifolds

Michele Caselli, Enric Florit-Simon, Joaquim Serra

This article studies the canonical Hilbert energy $H^{s /2} (M)$ on a Riemannian manifold for $s \in (0, 2)$ , with particular focus on the case of closed manifolds. Several equivalent d…

Finite index solutions to the Bernoulli problem in three dimensions are axially symmetric

Phase transitions with bounded index: Parallels to De Giorgi's conjecture

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

Fractional Sobolev spaces on Riemannian manifolds

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