An infinity laplace equation with gradient term and mixed boundary conditions

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

doi:10.1090/S0002-9939-2010-10666-4

An infinity laplace equation with gradient term and mixed boundary conditions

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

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	1763-1776
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	5
DOIs	https://doi.org/10.1090/S0002-9939-2010-10666-4
State	Published - May 2011

Keywords

Comparison principle
Infinity laplace equation

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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