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arXiv · 1402.5746

Maximal estimates for Schroedinger equation with inverse-square potential

Changxing Miao·Junyong Zhang·Jiqiang Zheng
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Abstract

In this paper, we consider the maximal estimates for the solution to an initial value problem of the linear Schroedinger equation with a singular potential. We show a result about the pointwise convergence of solutions to this special variable coefficient Schroedinger equation with initial data $u_0\in H^{s}(\R^n)$ for $s>1/2$ or radial initial data $u_0\in H^{s}(\R^n)$ for $s\geq1/4$ and the solution does not converge when $s<1/4$.

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Changxing Miao, Junyong Zhang, Jiqiang Zheng. 2014-02-24. Maximal estimates for Schroedinger equation with inverse-square potential. https://doi.org/10.2140/pjm.2015.273.1

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