On the comparison principle for unbounded solutions of elliptic equations with first order terms

We prove a comparison principle for unbounded weak sub/super solutions of the equationλu−div(A(x)Du)=H(x,Du) in Ω where A(x) is a bounded coercive matrix with measurable ingredients, λ≥0 and ξ↦H(x,ξ) has a super linear growth and is convex at infinity. We improve earlier results where the convexity of H(x,⋅) was required to hold globally.