TY - JOUR
T1 - An infinity laplace equation with gradient term and mixed boundary conditions
AU - Armstrong, Scott N.
AU - Smart, Charles K.
AU - Somersille, Stephanie J.
PY - 2011/5
Y1 - 2011/5
N2 - 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.
AB - 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.
KW - Comparison principle
KW - Infinity laplace equation
UR - http://www.scopus.com/inward/record.url?scp=79952182939&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79952182939&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2010-10666-4
DO - 10.1090/S0002-9939-2010-10666-4
M3 - Article
AN - SCOPUS:79952182939
VL - 139
SP - 1763
EP - 1776
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 5
ER -