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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An infinity Laplace equation with gradient term and mixed boundary conditions
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by Scott N. Armstrong, Charles K. Smart and Stephanie J. Somersille PDF
Proc. Amer. Math. Soc. 139 (2011), 1763-1776 Request permission

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.
References
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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
  • MR Author ID: 893148
  • Email: smart@math.berkeley.edu
  • Stephanie J. Somersille
  • Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
  • Email: steph@math.utexas.edu
  • 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