An infinity Laplace equation with gradient term and mixed boundary conditions

Details An infinity Laplace equation with gradient term and mixed boundary conditions An infinity Laplace equation with gradient term and mixed boundary conditions

2009-10-20

arxiv.org/abs/0910.3744v2

Mathematics

Analysis of PDEs

13 pages, minor mistakes and typos corrected

Scientific paper

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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