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Rendiconti Lincei - Matematica e Applicazioni


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Volume 26, Issue 4, 2015, pp. 433–443
DOI: 10.4171/RLM/714

Published online: 2015-10-29

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

Armin Schikorra[1], Tien-Tsan Shieh[2] and Daniel Spector[3]

(1) Albert-Ludwigs-Universit├Ąt Freiburg, Germany
(2) National Central University, Chung Li, Taiwan
(3) National Chiao Tung University, Hsinchu, Taiwan

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.

Keywords: Fractional elliptic PDE, VMO coefficients, commutators

Schikorra Armin, Shieh Tien-Tsan, Spector Daniel: $L^p$ theory for fractional gradient PDE with $VMO$ coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), 433-443. doi: 10.4171/RLM/714