Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 77, pp. 1-12.
Title: Infinity Laplace equation with non-trivial right-hand side
Authors: Guozhen Lu (Wayne State Univ., Detroit, MI, USA)
Peiyong Wang (Wayne State Univ., Detroit, MI, USA)
Abstract:
We analyze the set of continuous viscosity solutions of
the infinity Laplace equation $-\Delta^N_{\infty}w(x) = f(x)$,
with generally sign-changing right-hand side in a bounded domain.
The existence of a least and a greatest continuous viscosity
solutions, up to the boundary, is proved through a Perron's
construction by means of a strict comparison principle. These
extremal solutions are proved to be absolutely extremal solutions.
Submitted July 2, 2009. Published June 08, 2010.
Math Subject Classifications: 35J70, 35B35.
Key Words: Infinity Laplace equation; inhomogeneous equation;
viscosity solutions; least solution; greatest solution;
strict comparison principle; existence; uniqueness;
local Lipschitz continuity.