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• W2952634281 abstract "In this paper we derive a strong maximum principle for weak supersolutions of nonlocal equations of the form $Iu=c(x) u$ in $Omega$, where $Omegasubset mathbb{R}^N$ is a domain, $cin L^{infty}(Omega)$ and $I$ is an operator of the form $Iu(x)=P.V.int_{mathbb{R}^N}(u(x)-u(y))j(x-y) dy$ with a nonnegative kernel function $j$. We formulate minimal positivity assumptions on $j$ corresponding to a class of operators which includes highly anisotropic variants of the fractional Laplacian. Somewhat surprisingly, this problem leads to the study of general lattices in $mathbb{R}^N$. Our results extend to the regional variant of the operator $I$ and, under weak additional assumptions, also to the case of $x$-dependent kernel functions." @default.
• W2952634281 created "2019-06-27" @default.
• W2952634281 creator A5045719093 @default.
• W2952634281 creator A5062208839 @default.
• W2952634281 date "2017-02-28" @default.
• W2952634281 modified "2023-09-27" @default.
• W2952634281 title "On the strong maximum principle for nonlocal operators" @default.
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• W2952634281 hasPublicationYear "2017" @default.
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