Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions

In this note we present some uniqueness and comparison results for a class of problem of the form(0.1)−Lu=H(x,u,∇u)+h(x),u∈H01(Ω)∩L∞(Ω), where Ω⊂RN, N≥2 is a bounded domain, L is a general elliptic second order linear operator with bounded coefficients and H is allowed to have a critical growth in the gradient. In some cases our assumptions prove to be sharp.