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http://hdl.handle.net/2445/194027
Title: | The Boundary Harnack Principle for Nonlocal Elliptic Operators in Non-divergence Form |
Author: | Ros, Xavier Serra Montolí, Joaquim |
Keywords: | Teoria d'operadors Equacions diferencials parcials estocàstiques Processos estocàstics Anàlisi global (Matemàtica) Operator theory Stochastic partial differential equations Stochastic processes Global analysis (Mathematics) |
Issue Date: | Oct-2019 |
Publisher: | Springer Verlag |
Abstract: | 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 $L u_1=$ $L u_2=0$ 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1007/s11118-018-9713-7 |
It is part of: | Potential Analysis, 2019, vol. 51, p. 315-331 |
URI: | http://hdl.handle.net/2445/194027 |
Related resource: | https://doi.org/10.1007/s11118-018-9713-7 |
ISSN: | 0926-2601 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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