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

Krzysztof Bogdan, Jacek Dziubański, Karol Szczypkowski

We give new sufficient conditions for comparability of the fundamental solution of the Schrödinger equation ${\partial }_t=\Delta +V$ with the Gauss-Weierstrass kernel and show that local $…