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 equation λ u − div ( A ( x ) D u ) = H ( x , D u ) 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. [ABSTRACT FROM AUTHOR]