# $L^p$-theory for fractional gradient PDE with VMO coefficients

created by spector on 25 Mar 2015
modified on 12 Oct 2015

[BibTeX]

Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.

Inserted: 25 mar 2015
Last Updated: 12 oct 2015

Pages: 10
Year: 2015

Abstract:

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.