Local $L^p$ norms of Schr{\"o}dinger eigenfunctions on $\mathbb{S}^2$

Gabriel Rivière

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arXiv · 2012.08838

Local $L^p$ norms of Schr{\"o}dinger eigenfunctions on $\mathbb{S}^2$

Gabriel Rivière

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Abstract

On the canonical $2$-sphere and for Schr{\"o}dinger 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.

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Gabriel Rivière. 2020-12-16. Local $L^p$ norms of Schr{\"o}dinger eigenfunctions on $\mathbb{S}^2$. https://arxiv.org/abs/2012.08838

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