The poisson equation from non-local to local
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Fecha
2018
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Texas State University - San Marcos
Resumen
We 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.
Palabras clave
Elliptic equations
Fractional laplacian
Weak solutions
Fractional laplacian
Weak solutions
Descripción
Materias
Cita
Biccari, U., & Hernández-Santamaría, V. (2018). The poisson equation from non-local to local. Electronic Journal of Differential Equations, 2018(145), 1-13.