JournalsrlmVol. 26, No. 4pp. 433–443

LpL^p theory for fractional gradient PDE with VMOVMO 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
$L^p$ theory for fractional gradient PDE with $VMO$ coefficients cover
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Abstract

In this paper, we prove LpL^p estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are VMOVMO. 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, LpL^p theory for fractional gradient PDE with VMOVMO coefficients. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 4, pp. 433–443

DOI 10.4171/RLM/714