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|Du|h△∞u=f, where 0≤h≤20≤h≤2 and △∞u△∞u denotes the so-called infinity Laplacian operator given by △∞u=∑i,j=1n∂u∂xi∂u∂xj∂2u∂xi∂xj. We also give an asymptotic behavior of the viscosity solutions of two kinds of inhomogeneous infinity Laplace equations near an isolated singular point.