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.