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.
Original language | English (US) |
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Pages (from-to) | 1763-1776 |
Number of pages | 14 |
Journal | Proceedings of the American Mathematical Society |
Volume | 139 |
Issue number | 5 |
DOIs | |
State | Published - May 2011 |
Keywords
- Comparison principle
- Infinity laplace equation
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics