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arXiv · 1104.5367

Global estimates of fundamental solutions for higher-order Schr\"odinger equations

JinMyong Kim·Anton Arnold·Xiaohua Yao
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Abstract

In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schr\"odinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish related Lp-Lq estimates on the Schr\"odinger solution. These estimates extend known results from the literature and are sharp. This result was latetly already generalized to a degenerate case (cf. [9]).

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JinMyong Kim, Anton Arnold, Xiaohua Yao. 2011-04-28. Global estimates of fundamental solutions for higher-order Schr\"odinger equations. https://doi.org/10.1007/s00605-011-0350-0

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