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An infinity Laplace equation with gradient term and mixed boundary conditions. (English) Zbl 1216.35062

Summary: 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.

MSC:

35J70 Degenerate elliptic equations
35J75 Singular elliptic equations
91A15 Stochastic games, stochastic differential games
35J25 Boundary value problems for second-order elliptic equations
35B51 Comparison principles in context of PDEs
35B35 Stability in context of PDEs
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