Gaussian lower bound for the Neumann Green function of a general parabolic operator

Abstract

Based on the fact that the Neumann Green function can be constructed as a perturbation of the fundamental solution by a single-layer potential, we establish a Gaussian lower bound for the Neumann Green function for a general parabolic operator. We build our analysis on classical tools coming from the construction of a fundamental solution of a general parabolic operator by means of the so-called parametrix method. At the same time we provide a simple proof for Gaussian two-sided bounds for the fundamental solution.