Solutions to an inhomogeneous equation involving infinity Laplacian

We obtain existence and uniqueness results of viscosity solutions to the Dirichlet boundary value problem for a nonlinear highly degenerate elliptic equation of the form 1/vertical bar Du vertical bar(h)Delta(infinity) u = f, where 0 <= h <= 2 and Delta(infinity) u denotes the so-called infinity Laplacian operator given by Delta(infinity) u = Sigma(n)(i,j=1) partial derivative u/partial derivative x(i) partial derivative u/partial derivative x(j) partial derivative(2)u/partial derivative x(i)partial derivative x(j). We also give an asymptotic behavior of the viscosity solutions of two kinds of inhomogeneous infinity Laplace equations near an isolated singular point. (C) 2012 Elsevier Ltd. All rights reserved.