Biccari, UmbertoHernández Santamaría, Víctor2025-01-072025-01-072018Biccari, U., & Hernández-Santamaría, V. (2018). The poisson equation from non-local to local. Electronic Journal of Differential Equations, 2018(145), 1-13.http://hdl.handle.net/20.500.14454/2193We analyze the limiting behavior as s → 1− of the solution to the fractional Poisson equation (−∆)s us = fs, x ∈ Ω with homogeneous Dirichlet boundary conditions us ≡ 0, x ∈ Ωc. We show that lims →1 − us = u, with −∆u = f, x ∈ Ω and u = 0, x ∈ ∂Ω. Our results are complemented by a discussion on the rate of convergence and on extensions to the parabolic setting.eng© 2018 Texas State UniversityElliptic equationsFractional laplacianWeak solutionsjournal article2025-01-071072-6691