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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An infinity Laplace equation with gradient term and mixed boundary conditions


Authors: Scott N. Armstrong, Charles K. Smart and Stephanie J. Somersille
Journal: Proc. Amer. Math. Soc. 139 (2011), 1763-1776
MSC (2010): Primary 35J70, 35J75, 91A15
Published electronically: October 29, 2010
MathSciNet review: 2763764
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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain existence, uniqueness, and stability results for the modified 1-homogeneous infinity Laplace equation

$\displaystyle -\Delta_\infty u -\beta \vert Du\vert = 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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Additional Information

Scott N. Armstrong
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: armstrong@math.lsu.edu

Charles K. Smart
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: smart@math.berkeley.edu

Stephanie J. Somersille
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
Email: steph@math.utexas.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10666-4
PII: S 0002-9939(2010)10666-4
Keywords: Infinity Laplace equation, comparison principle
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.