THE LIMIT AS p →∞ IN A NONLOCAL p−LAPLACIAN EVOLUTION EQUATION. A NONLOCAL APPROXIMATION OF A MODEL FOR SANDPILES

@inproceedings{Mazn2007THELA,
  title={THE LIMIT AS p →∞ IN A NONLOCAL p−LAPLACIAN EVOLUTION EQUATION. A NONLOCAL APPROXIMATION OF A MODEL FOR SANDPILES},
  author={Jos{\'e} M. Maz{\'o}n and Julio D. Rossi and Juli{\'a}n Toledo},
  year={2007}
}
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, ut(t, x) = ∫ RN J(x− y)|u(t, y)− u(t, x)|p−2(u(t, y)− u(t, x)) dy. We prove existence and uniqueness of a limit solution that verifies an equation governed by the subdifferetial of a convex energy functional associated to the indicator function of the set K = {u ∈ L(R ) : |u(x)−u(y)| ≤ 1, when x− y ∈ supp(J)}. We also find some explicit… CONTINUE READING

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