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
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 


Luis Silvestre's work (e.g., Hölder estimates for solutions of integro differential equations like the fractional laplace, Indiana Univ. Math. J. 55 (2006), 11551174) and classical potential theory estimates, taken together, give you $C^\alpha$ Hölder type regularity. Assuming, that is, that s is not too large. 

