Convex Hypersurfaces and $L^p$ Estimates for Schr\"odinger Equations

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Zheng, Quan; Yao, Xiaohua; Fan, Da;
  • Subject: 42B10 | Mathematics - Classical Analysis and ODEs | Mathematics - Analysis of PDEs | 35J10

This paper is concerned with Schr\"odinger 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... View more
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