Green's function estimates for time measurable parabolic operators on polyhedrons and polyhedral cones

We provide Green’s function estimates for parabolic operators on polyhedrons and polyhedral cones in ${\mathbb{R}}^3$. These estimates incorporate mixed weights, which include appropriate powers of the distances to the vertices, the edges, and the boundary of the domains. The allowable ranges for the weight parameters are explicitly determined by the geometry of the domains.