In this paper, we prove estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are . In particular, our work extends the optimal regularity known in the second order elliptic setting to a spectrum of fractional order elliptic equations.
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Armin Schikorra, Tien-Tsan Shieh, Daniel Spector, theory for fractional gradient PDE with coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 4, pp. 433–443DOI 10.4171/RLM/714