Global tangential Calderon-Zygmund type estimates for the regional fractional Laplacian
Sujin Khomrutai, Armin Schikorra, Adisak Seesanea, Sasikarn Yeepo
TL;DR
This paper develops boundary tangential Sobolev estimates for solutions to the regional fractional Laplacian, enabling reduction of complex boundary problems to simpler one-dimensional nonlocal problems.
Contribution
It introduces a novel approach to boundary estimates for the regional fractional Laplacian, facilitating dimensional reduction in boundary Calderon-Zygmund theory.
Findings
Establishment of tangential Sobolev estimates up to the boundary.
Reduction of boundary Calderon-Zygmund problems to one-dimensional nonlocal problems.
Framework applicable to higher-dimensional boundary analysis.
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.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Partial Differential Equations · Spectral Theory in Mathematical Physics