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An infinity Laplace equation with gradient term and mixed boundary conditions
2011
Proceedings of the American Mathematical Society
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We obtain existence, uniqueness, and stability results for the modified 1-homogeneous infinity Laplace equation 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.
doi:10.1090/s0002-9939-2010-10666-4
fatcat:i4iygpvqpzc75hgpotphy6hlmm