Abstract
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.
Highlights
The qualitative theory of second-order elliptic equations received a strong effort from Harnack inequalities
For the sake of completeness, we show the basic weak Harnack inequality and local MP for a uniformly elliptic operator with an additive first-order term having linear growth in the gradient
We say that an open connected set Ω of Rn is a G domain if to each y ∈ Ω we can associate a ball B BR xy of radius R ≤ R0 such that y ∈ BτR xy, B \ Ωy ≥ σ|B|, Gσ,τ
Summary
The qualitative theory of second-order elliptic equations received a strong effort from Harnack inequalities. R f − Ln BR∩A , 3.25 with a positive constant C, depending on n, λ, Λ, q, τ, b0Nq−1R2−q, and p
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