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

Armin Schikorra; Tien-Tsan Shieh; Daniel Spector

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

Analysis of PDEs 2015-03-26 v1 Functional Analysis

Authors: Armin Schikorra , Tien-Tsan Shieh , Daniel Spector

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.

Keywords

fractional PDE L^p estimates VMO coefficients elliptic equations fractional derivatives optimal regularity

Cite

@article{arxiv.1503.07318,
  title  = {$L^p$-theory for fractional gradient PDE with VMO coefficients},
  author = {Armin Schikorra and Tien-Tsan Shieh and Daniel Spector},
  journal= {arXiv preprint arXiv:1503.07318},
  year   = {2015}
}

Comments

10 pages

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