An infinity Laplace equation with gradient term and mixed boundary conditions

Armstrong, Scott; Smart, Charles; Somersille, Stephanie

doi:10.1090/S0002-9939-2010-10666-4

An infinity Laplace equation with gradient term and mixed boundary conditions
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by Scott N. Armstrong, Charles K. Smart and Stephanie J. Somersille PDF

Proc. Amer. Math. Soc. 139 (2011), 1763-1776 Request permission

Abstract:

We obtain existence, uniqueness, and stability results for the modified 1-homogeneous infinity Laplace equation \[ -\Delta _\infty u -\beta |Du| = f, \] subject to Dirichlet or mixed Dirichlet-Neumann boundary conditions. Our arguments rely on comparing solutions of the PDE to subsolutions and supersolutions of a certain finite difference approximation.

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