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arXiv · 1511.07167

Sharp Gaussian estimates for Schrödinger heat kernels: $L^p$ integrability conditions

Krzysztof Bogdan·Jacek Dziubański·Karol Szczypkowski
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Abstract

We give new sufficient conditions for comparability of the fundamental solution of the Schrödinger equation $\partial_t=Δ+V$ with the Gauss-Weierstrass kernel and show that local $L^p$ integrability of $V$ for $p> 1$ is not necessary for the comparability.

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Krzysztof Bogdan, Jacek Dziubański, Karol Szczypkowski. 2016-09-08. Sharp Gaussian estimates for Schrödinger heat kernels: $L^p$ integrability conditions. https://arxiv.org/abs/1511.07167

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