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Hey, I want to know what is the best interior regularity of the following equaiton:

$(-\Delta)^{\frac{s}{2}}u=f$ in $B_{1}$ (ball with radius 1, centered at 0) $f\in L^{\infty}(B_1)$

thanks

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  • $\begingroup$ What is the regularity of $f$ in $B_1\setminus B_{1/2}$ ? $\endgroup$
    – Denis Serre
    Commented Jan 5, 2011 at 18:37

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Luis Silvestre's work (e.g., Hölder estimates for solutions of integro differential equations like the fractional laplace, Indiana Univ. Math. J. 55 (2006), 1155-1174) and classical potential theory estimates, taken together, give you $C^\alpha$ Hölder type regularity. Assuming, that is, that s is not too large.

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