The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary |
| |
Authors: | Xavier Ros-Oton Joaquim Serra |
| |
Institution: | Universitat Politècnica de Catalunya, Departament de Matemàtica Aplicada I, Diagonal 647, 08028 Barcelona, Spain |
| |
Abstract: | 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 (−Δ)su=g in Ω , u≡0 in Rn\Ω, for some s∈(0,1) and g∈L∞(Ω), then u is Cs(Rn) and u/δs|Ω is Cα 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. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|