An infinity laplace equation with gradient term and mixed boundary conditions

Scott N. Armstrong, Charles K. Smart, Stephanie J. Somersille

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)1763-1776
Number of pages14
JournalProceedings of the American Mathematical Society
Volume139
Issue number5
DOIs
StatePublished - May 2011

Keywords

  • Comparison principle
  • Infinity laplace equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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