Semigrupos gerados pelo p-Laplaciano e um estudo do limite p→∞

Abstract

We study the problem: (2) _∂tup − Δpup = 0, (0,∞) × Rd up(0, x) = g(x), {t = 0} × Rd ∞ > p ≥ d+1, where the initial data up(0, x) = g(x) are Lipschitz continuous, non-negative and it have compact support. Solutions of this problem provide a simplistic model for collapse of an initially unstable sandpile . We regard the limit up when p→∞as a solution for instantaneous mass transfer problem governed by Monge-Kantorovich theory. We study the case d = 1 for which we obtain explicit solutions. Keywords: p-laplacian, Monge-Kantorovich Theory, Monotone operator theory.