$L^p$ theory for fractional gradient PDE with $VMO$ coefficients
$L^p$ theory for fractional gradient PDE with $VMO$ coefficients
In this paper, we prove L^p estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are VMO . In particular, our work extends the optimal regularity known in the second order elliptic setting to a spectrum of fractional order elliptic equations.