We study the heat kernel and the Green’s function on the infinite supercritical percolation cluster in dimension d ≥ 2 and prove a quantitative homogenization theorem for these functions with an ...

Let $L$ be a linear, second order parabolic operator in divergence form and let $U$ be a bounded domain in $E^{n + 1}$. The Dirichlet problem for $Lu = 0$ is solved ...