Convex Hypersurfaces and L Estimates for Schrödinger Equations
نویسنده
چکیده
This paper is concerned with Schrödinger equations whose principal operators are homogeneous elliptic. When the corresponding level hypersurface is convex, we show the Lp-Lq estimate of solution operator in free case. This estimate, combining with the results of fractionally integrated groups, allows us to further obtain the Lp estimate of solutions for the initial data belonging to a dense subset of Lp in the case of integrable potentials. This project was supported by the National Science Foundation of China 2000 Mathematics Subject Classification: Primary 35J10; Secondary 42B10, 47D62
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