Existence of a unique solution to a quasilinear elliptic equation

The purpose of this paper is to prove the existence of a unique classical solution u(x) to the quasilinear elliptic equation −∇ · (a(u)∇u) + v · ∇u = f , where u(x0) = u0 at x0 ∈ Ω and where n · ∇u = g on the boundary ∂Ω. We prove that if the functions a, f , v, g satisfy certain conditions, then a unique classical solution u(x) exists. Applications include stationary heat/diffusion problems with convection and with a source/sink, where the value of the solution is known at a spatial location x0 ∈ Ω, and where n · ∇u is known on the boundary.