We provide a Hopf boundary lemma for the regional fractional Laplacian (-Delta)(Omega)(s), with Omega subset of R-N a bounded open set. More precisely, given u a pointwise or weak super-solution of the equation (-Delta)(Omega)(s)u = c(x)u in Omega, we show that the ratio u(x)/(dist(x, partial derivative Omega))(2s-1) is strictly positive as x approaches the boundary partial derivative Omega of Omega. We also prove a strong maximum principle for distributional super-solutions.
Abatangelo N., Fall M.M., Temgoua R.Y. (2023). A Hopf lemma for the regional fractional Laplacian. ANNALI DI MATEMATICA PURA ED APPLICATA, 202(1), 95-113 [10.1007/s10231-022-01234-6].
A Hopf lemma for the regional fractional Laplacian
Abatangelo N.;
2023
Abstract
We provide a Hopf boundary lemma for the regional fractional Laplacian (-Delta)(Omega)(s), with Omega subset of R-N a bounded open set. More precisely, given u a pointwise or weak super-solution of the equation (-Delta)(Omega)(s)u = c(x)u in Omega, we show that the ratio u(x)/(dist(x, partial derivative Omega))(2s-1) is strictly positive as x approaches the boundary partial derivative Omega of Omega. We also prove a strong maximum principle for distributional super-solutions.| File | Dimensione | Formato | |
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