Solutions to an inhomogeneous equation involving Aronsson operator

Let F:Rn→[0,+∞)F:Rn→[0,+∞) be a convex function of class C2(Rn∖{0})C2(Rn∖{0}), which is positively homogeneous of degree 1, we assume further that F(p)>0F(p)>0 for any p≠0p≠0, and Hess(F2) is positive definite in Rn∖{0}Rn∖{0}. In this paper, for a bounded domain Ω⊂RnΩ⊂Rn, f∈C(Ω)f∈C(Ω) with infΩf(x)>0infΩf(x)>0 and g∈C(∂Ω)g∈C(∂Ω), we obtain existence and uniqueness results of viscosity solutions to the Dirichlet boundary value problem for a nonlinearly highly degenerate elliptic equation of the form{1[F(Du)]hAu=f,in Ωu=g,on ∂Ω where AA denotes the Aronsson operator given by Au=∑i,j=1n∂2u∂xi∂xj∂(12F2)∂pi(Du)∂(12F2)∂pj(Du) and 0≤h<20≤h<2.