The Poisson equation from non-local to local
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We analyze the limiting behavior as s → 1¯ of the solution to the fractional Poisson equation (-∆)sus = ƒs, x ∈ Ω with homogeneous Dirichlet boundary conditions us ≡ 0, x ∈ Ωc. We show that lims→1¯ us = 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.
CitationBiccari, U., & Hernández-Santamaría, V. (2018). The Poisson equation from non-local to local. Electronic Journal of Differential Equations, 2018(145), pp. 1-13.
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