Local Elliptic Regularity for the Dirichlet Fractional Laplacian
نویسندگان
چکیده
منابع مشابه
The Dirichlet Problem for the Fractional Laplacian: Regularity up to the Boundary
We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u is a solution of (−∆)u = g in Ω, u ≡ 0 in R\Ω, for some s ∈ (0, 1) and g ∈ L∞(Ω), then u is C(R) and u/δ|Ω is C up to the boundary ∂Ω for some α ∈ (0, 1), where δ(x) = dist(x, ∂Ω). For this, we develop a fractional analog of the Krylov boundary Harnack method. Moreov...
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ژورنال
عنوان ژورنال: Advanced Nonlinear Studies
سال: 2017
ISSN: 1536-1365,2169-0375
DOI: 10.1515/ans-2017-0014