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Convex Hypersurfaces and $L^p$ Estimates for Schrödinger Equations

Quan Zheng·Xiaohua Yao·Da Fan
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Abstract

This paper is concerned with Schrödinger equations whose principal operators are homogeneous elliptic. When the corresponding level hypersurface is convex, we show the $L^p$-$L^q$ estimate of solution operator in free case. This estimate, combining with the results of fractionally integrated groups, allows us to further obtain the $L^p$ estimate of solutions for the initial data belonging to a dense subset of $L^p$ in the case of integrable potentials.

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Quan Zheng, Xiaohua Yao, Da Fan. 2004-04-27. Convex Hypersurfaces and $L^p$ Estimates for Schrödinger Equations. https://arxiv.org/abs/math/0403321

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