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- W4295312754 abstract "We establish sharp boundary regularity estimates in $C^1$ and $C^{1,alpha}$ domains for nonlocal problems of the form $Lu=f$ in $Omega$, $u=0$ in $Omega^c$. Here, $L$ is a nonlocal elliptic operator of order $2s$, with $sin(0,1)$. First, in $C^{1,alpha}$ domains we show that all solutions $u$ are $C^s$ up to the boundary and that $u/d^sin C^alpha(barOmega)$, where $d$ is the distance to $partialOmega$. In $C^1$ domains, solutions are in general not comparable to $d^s$, and we prove a boundary Harnack principle in such domains. Namely, we show that if $u_1$ and $u_2$ are positive solutions, then $u_1/u_2$ is bounded and Holder continuous up to the boundary. Finally, we establish analogous results for nonlocal equations with bounded measurable coefficients in non-divergence form. All these regularity results will be essential tools in a forthcoming work on free boundary problems for nonlocal elliptic operators cite{CRS-obstacle}." @default.
- W4295312754 created "2022-09-12" @default.
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- W4295312754 date "2015-12-22" @default.
- W4295312754 modified "2023-10-18" @default.
- W4295312754 title "Boundary regularity estimates for nonlocal elliptic equations in $C^1$ and $C^{1,alpha}$ domains" @default.
- W4295312754 doi "https://doi.org/10.48550/arxiv.1512.07171" @default.
- W4295312754 hasPublicationYear "2015" @default.
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