Nonlocal diffusion equations in Carnot groups

Let G be a Carnot group. We study nonlocal diffusion equations in a domain Omega of G of the form u(t)(epsilon)(x, t) = integral(G)1/epsilon(2) K-epsilon(x,y)(u(epsilon)(y,t) - u(epsilon)(x,t)) dy, x is an element of Omega with u(epsilon) = g(x, t) for x is not an element of Omega. For an appropriated resealed kernel K-epsilon, we apply the Taylor series development in Carnot groups in order to prove that the solutions u(epsilon) uniformly approximate the solution of a certain local Dirichlet problem in Omega, when epsilon -> 0.