Global tangential Calderon-Zygmund type estimates for the regional fractional Laplacian

2022/09/16 by Khomrutai, Sujin, Schikorra, Armin, Seesanea, Adisak +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.07939

Abstract

We discuss tangential Sobolev-estimates up to the boundary for solutions to the regional fractional laplacian on the upper half-plane. These estimates can be used to reduce the boundary Calderon-Zygmund theory of any dimension to a one-dimensional nonlocal problem.

Related

• Global Calderón-Zygmund theory for fractional Laplacian type equations
• Calderón-Zygmund estimates for the fractional p-Laplacian
• The eigenvalue problem for the regional fractional Laplacian in the small order limit
• On the sharp constants in the regional fractional Sobolev inequalities
• Pohozaev-like identity for the regional fractional laplacian