Let $G$ be the Green function of the Fractional Laplacian $(-\Delta)^s$ in a domain $\Omega$ (which is known explicitly for the special case of the ball: link). Does $\nabla_x G(0,z)$ satisfy $$(-\Delta)^s\nabla_x G(0,z) = 0 \text{ in } \Omega \ ?$$ In other words I'm asking if $\nabla_x$ and $(-\Delta)^s$ commute on a bounded domain $\Omega$
2026-03-28 11:34:22.1774697662
Derivative of Green function of Fractional Laplacian
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