3 papers
math.AP2026
A logistic equation with non-local operators of order near zero
Luigi Appolloni, Serena Dipierro, Enrico Valdinoci
In this paper we study an equation driven by a non-local operator of order "near zero" with mixed Dirichlet-Neumann boundary conditions, modelling a biological system consisting of…
math.AP2025
Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains
Luigi Appolloni, Riccardo Molle
We consider the problem , where verifies , and . Here, is nonempty and compact. We…
math.AP2025
A Note on Moving Frames along Sobolev Maps and the Regularity of Weakly Harmonic Maps
Luigi Appolloni, Ben Sharp
The purpose of this note is twofold. First we show that, for weakly differentiable maps between Riemannian manifolds of any dimension, a smallness condition on a Morrey-norm of the…