Abstract: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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- Scott N. Armstrong
- Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
- Email: firstname.lastname@example.org
- Charles K. Smart
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- MR Author ID: 893148
- Email: email@example.com
- Stephanie J. Somersille
- Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
- Email: firstname.lastname@example.org
- Received by editor(s): November 1, 2009
- Received by editor(s) in revised form: May 23, 2010
- Published electronically: October 29, 2010
- Communicated by: Matthew J. Gursky
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 139 (2011), 1763-1776
- MSC (2010): Primary 35J70, 35J75, 91A15
- DOI: https://doi.org/10.1090/S0002-9939-2010-10666-4
- MathSciNet review: 2763764