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arXiv · 1710.07404

Global uniqueness for the semilinear fractional Schr\"odinger equation

Ru-Yu Lai·Yi-Hsuan Lin
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Abstract

We study global uniqueness in an inverse problem for the fractional semilinear Schr\"{o}dinger equation $(-\Delta)^{s}u+q(x,u)=0$ with $s\in (0,1)$. We show that an unknown function $q(x,u)$ can be uniquely determined by the Cauchy data set. In particular, this result holds for any space dimension greater than or equal to $2$. Moreover, we demonstrate the comparison principle and provide a $L^\infty$ estimate for this nonlocal equation under appropriate regularity assumptions.

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Ru-Yu Lai, Yi-Hsuan Lin. 2017-10-20. Global uniqueness for the semilinear fractional Schr\"odinger equation. https://arxiv.org/abs/1710.07404

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