On the trace of the wave group and regularity of potentials

IF 0.8 4区数学 Q2 MATHEMATICS

Annales De L Institut Fourier Pub Date : 2021-04-02 DOI:10.5802/aif.3538

Hart F. Smith

引用次数: 0

Abstract

For the wave equation $\partial_t^2-\Delta+V$ on $\mathbb{R}^d$ with compactly supported, real valued potential $V$, we establish a sharp relation between Sobolev regularity of $V$ and the existence of finite order expansions as $t\rightarrow 0$ for the relative trace of the wave group.

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论波群的迹和势的规律性

对于具有紧支撑实值势$V$的$\mathbb{R}^d$上的波动方程$\partial_t^2-\Delta+V$，我们建立了$V$的Sobolev正则性与波群相对轨迹的有限阶展开式$t\rightarrow 0$的存在之间的密切关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales De L Institut Fourier 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

1 months

期刊介绍： The Annales de l’Institut Fourier aim at publishing original papers of a high level in all fields of mathematics, either in English or in French. The Editorial Board encourages submission of articles containing an original and important result, or presenting a new proof of a central result in a domain of mathematics. Also, the Annales de l’Institut Fourier being a general purpose journal, highly specialized articles can only be accepted if their exposition makes them accessible to a larger audience.