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

Armin Schikorra; Tien-Tsan Shieh; Daniel Spector

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arXiv · 1503.07318

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

Armin Schikorra·Tien-Tsan Shieh·Daniel Spector

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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 $VMO$. 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. 2015-03-25. $L^p$-theory for fractional gradient PDE with VMO coefficients. https://arxiv.org/abs/1503.07318

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