Global estimates of fundamental solutions for higher-order Schrödinger equations
Global estimates of fundamental solutions for higher-order Schrödinger equations
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DOI：
10.1007/s00605-011-0350-0
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发表时间：
2011-04
期刊：
影响因子：
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通讯作者：
Jinmyong Kim;A. Arnold;X. Yao
中科院分区：
文献类型：
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作者：
Jinmyong Kim;A. Arnold;X. Yao
本文首先建立了薛定谔方程基本解的整体点态时空估计，其中空间算子的符号是一个真实的非退化椭圆多项式。然后我们使用这样的估计建立薛定谔解的相关Lp-Lq估计。这些估计扩展了文献中的已知结果，并且是尖锐的。这个结果最近已经推广到退化的情况下（参见。[4]）。
In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schrödinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish relatedLp–Lqestimates on the Schrödinger solution. These estimates extend known results from the literature and are sharp. This result was lately already generalized to a degenerate case (cf. [4]).