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arXiv:0910.3744 [math.AP]AbstractReferencesReviewsResources

An infinity Laplace equation with gradient term and mixed boundary conditions

Scott N. Armstrong, Charles K. Smart, Stephanie J. Somersille

Published 2009-10-20, updated 2009-10-29Version 2

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.

Comments: 13 pages, minor mistakes and typos corrected
Categories: math.AP
Subjects: 35J70
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