Abstract. In this paper we study the nonlocal p-Laplacian-type diffusion equation ut(t, x) = ∫ RN J(x−y)|u(t, y)−u(t, x)|p−2(u(t, y)−u(t, x)) dy, (t, x) ∈]0, T [×Ω, with u(t, x) = ψ(x) for (t, x) ∈ ]0, T [×(RN \Ω). If p > 1, this is the nonlocal analogous problem to the well-known local p-Laplacian evolution equation ut = div(|∇u|p−2∇u) with Dirichlet boundary condition u(t, x) = ψ(x) on (t, x)...
