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

Armin Schikorra; Tien-Tsan Shieh; Daniel Spector

doi:10.4171/rlm/714

JournalsrlmVol. 26, No. 4pp. 433–443

$L^{p}$ theory for fractional gradient PDE with $V MO$ coefficients

Armin Schikorra
Albert-Ludwigs-Universität Freiburg, Germany
Tien-Tsan Shieh
National Central University, Chung Li, Taiwan
Daniel Spector
National Chiao Tung University, Hsinchu, Taiwan

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Abstract

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

Cite this article

Armin Schikorra, Tien-Tsan Shieh, Daniel Spector, $L^{p}$ theory for fractional gradient PDE with $V MO$ coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 4, pp. 433–443

DOI 10.4171/RLM/714