Local $L^p$ norms of Schrödinger eigenfunctions on $\mathbb{S}^2$

Gabriel Rivière (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

On the canonical $2$-sphere and for Schrödinger eigenfunctions, we obtain a simple geometric criterion on the potential under which we can improve, near a given point and for every $p\neq 6$, Sogge's estimates by a power of the eigenvalue. This criterion can be formulated in terms of the critical points of the Radon transform of the potential and it is independent of the choice of eigenfunctions.

Mots clés: Semiclassical analysis; completely integrable systems; global harmonic analysis

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Gabriel Rivière. Local $L^p$ norms of Schrödinger eigenfunctions on $\mathbb{S}^2$. Annales mathématiques du Québec, In press. ⟨hal-03065990v2⟩