Uniqueness of solution of Neumann problem for nonlinear elliptic equation

We prove, under assumptions lgρ(u)lgρ(u) concave and a(x,u,ξ)ρ(u) increasing in uu, existence and uniqueness of solutions u∈W1,p(Ω)∩L∞(Ω)u∈W1,p(Ω)∩L∞(Ω) to equations of the form −∑i=1n∂∂xi[ρ(u)bi(x,∂u∂x)]+a(x,u,∂u∂x)=0x∈Ω.