The Poisson equation from non-local to local
Date
2018-07-17
Authors
Biccari, Umberto
Hernandez-Santamaria, Victor
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
Fractional Laplacian, Elliptic equations, Weak solutions
Citation
Biccari, 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.
Rights
Attribution 4.0 International