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

Abstract

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 $L^p$ integrability of $V$ for $p>1$ is not necessary for the comparability.

arXiv comment13 pages, added Example 3.5, small editorial changes

Cited by in corpus (1)

• On the scattering problem for the nonlinear Schrödinger equation with a potential in 2D