# fa.practical evaluation – Fractional Laplacian equation on a ball and categorical options retort

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## fa.practical evaluation – Fractional Laplacian equation on a ball and categorical options

Let us assume
commence{align*} (-Delta)^s u &= 0 && x in B_r(0) u&=0 && x in mathbb R^N setminus B_r(0), stop{align*}
the place $$(-Delta)^s u(x) = int_{mathbb{R}^N} frac{u(x)-u(y)}{|x-y|^{N+2s}} dy,$$ ($$0)
is the fractional Laplacian. How can I discover options of this drawback within the design $$v(r)omega$$, with $$omega in S^{N-1}$$?

In a remark on Solution of the fractional Laplace equation on a ball, it was stated that the answer in $$B_r(0) setminus {0}$$ is
$$v(rho) = C_1rho(1-rho)^{s-1} + C_2 rho g(rho),$$ the place $$g(rho)$$ is the radial silhouette of the Green’s responsibility $$G(x,0)$$ in dimension $$N+2$$ and that to carry an answer of the issue on $$B_r(0)$$, we too necessity $$C_2 equiv 0$$. Is this rectify? How assassinate you show it?

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