Biccari, UmbertoHernandez-Santamaria, Victor2022-02-162022-02-162018-07-17Biccari, U., & Hernández-Santamaría, V. (2018). The Poisson equation from non-local to local. <i>Electronic Journal of Differential Equations, 2018</i>(145), pp. 1-13.1072-6691https://hdl.handle.net/10877/15345We analyze the limiting behavior as s → 1¯ of the solution to the fractional Poisson equation (-∆)s u s = ƒs, x ∈ Ω with homogeneous Dirichlet boundary conditions u s ≡ 0, x ∈ Ωc. We show that lim s→1¯ u s = u, with -∆u = ƒ, 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.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalFractional LaplacianElliptic equationsWeak solutionsArticle