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THE NEUMANN PROBLEM FOR THE ∞-LAPLACIAN AND THE MONGE-KANTOROVICH MASS TRANSFER PROBLEM
| Citations: | 26 - 17 self |
BibTeX
@MISC{García-azorero_theneumann,
author = {J. García-azorero and J. J. Manfredi and I. Peral and J. D. Rossi},
title = {THE NEUMANN PROBLEM FOR THE ∞-LAPLACIAN AND THE MONGE-KANTOROVICH MASS TRANSFER PROBLEM},
year = {}
}
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Abstract
Abstract. We consider the natural Neumann boundary condition for the ∞-Laplacian. We study the limit as p → ∞ of solutions of −∆pup = 0 in a domain Ω with |Dup | p−2 ∂up/∂ν = g on ∂Ω. We obtain a natural minimization problem that is verified by a limit point of {up} and a limit problem that is satisfied in the viscosity sense. It turns out that the limit variational problem is related to the Monge-Kantorovich mass transfer problems when the measures are supported on ∂Ω. 1. Introduction. In this paper we study the natural Neumann boundary conditions that appear when one considers the ∞-Laplacian in a smooth bounded domain as limit of the Neumann problem for the p-Laplacian as p → ∞. This problem is related to the Monge-Kantorovich mass tranfer problem when the involved measures are supported
