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An infinity Laplace equation with gradient term and mixed boundary conditions

By Scott N. Armstrong, Charles K. Smart, Stephanie, J. Somersille and Communicated Matthew J. Gursky

Abstract

Abstract. We obtain existence, uniqueness, and stability results for the modified 1-homogeneous infinity Laplace equation −Δ∞u − β|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. 1

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