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Harnack inequalities and ABP estimates for nonlinear second-order elliptic equations in unbounded domains. (English) Zbl 1187.35065

Summary: We are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient term. We look for local estimates, such as weak Harnack inequality and local maximum principle, and their extension up to the boundary. As applications, we deduce ABP-type estimates and weak maximum principles in general unbounded domains, a strong maximum principle, and a Liouville-type theorem.

MSC:

35J60 Nonlinear elliptic equations
35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35B50 Maximum principles in context of PDEs
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