Luigi Appolloni

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20202026

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math.AP2025

Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains

Luigi Appolloni, Riccardo Molle

We consider the problem $- Δ u + λ u = u^{p - 1}$ , where $u \in H_{0}^{1} (Ω)$ verifies $∥ u ∥_{L^{2}} = m > 0$ , and $λ \in [0, + \infty)$ . Here, $R^{N} ∖ Ω$ is nonempty and compact. We prove…

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…