The Boundary Harnack Principle for Nonlocal Elliptic Operators in Non-divergence Form
نویسنده
چکیده
We prove a boundary Harnack inequality for nonlocal elliptic operators L in non-divergence form with bounded measurable coefficients. Namely, our main result establishes that if Lu1 = Lu2 = 0 in Ω ∩ B1, u1 = u2 = 0 in B1 \ Ω, and u1, u2 ≥ 0 in R, then u1 and u2 are comparable in B1/2. The result applies to arbitrary open sets Ω. When Ω is Lipschitz, we show that the quotient u1/u2 is Hölder continuous up to the boundary in B1/2. These results will be used in forthcoming works on obstacle-type problems for nonlocal operators.
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