Ros, XavierSerra Montolí, Joaquim2023-02-232023-02-232019-100926-2601https://hdl.handle.net/2445/194027We 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 $L u_1=$ $L u_2=0$ in $\Omega \cap B_1, u_1=u_2=0$ in $B_1 \backslash \Omega$, and $u_1, u_2 \geq 0$ in $\mathbb{R}^n$, then $u_1$ and $u_2$ are comparable in $B_{1 / 2}$. The result applies to arbitrary open sets $\Omega$. When $\Omega$ is Lipschitz, we show that the quotient $u_1 / u_2$ is Hölder continuous up to the boundary in $B_{1 / 2}$. These results will be used in forthcoming works on obstacle-type problems for nonlocal operators.17 p.application/pdfeng(c) Springer Verlag, 2019Teoria d'operadorsEquacions diferencials parcials estocàstiquesProcessos estocàsticsAnàlisi global (Matemàtica)Operator theoryStochastic partial differential equationsStochastic processesGlobal analysis (Mathematics)info:eu-repo/semantics/article7085742023-02-23info:eu-repo/semantics/openAccess