The limit as p → ∞ in a nonlocal p -Laplacian evolution equation: a nonlocal approximation of a model for sandpiles

摘要

In this paper, we study the nonlocal ∞-Laplacian type diffusion equation obtained as the limit as p → ∞ to the nonlocal analogous to the p-Laplacian evolution, u_t (t,x) = ò_mathbbRN J(x-y)|u(t,y) - u(t,x)|p-2(u(t,y)- u(t,x)) dy.u_t (t,x) = int_{mathbb{R}^N} J(x-y)|u(t,y) - u(t,x)|^{p-2}(u(t,y)- u(t,x)) , dy.