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

Zheng, Quan; Yao, Xiaohua; Fan, Da

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

Authors

Zheng, Quan

Yao, Xiaohua

Fan, Da

Description

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.
18 pages