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arXiv · 1804.01067

An elliptic regularity theorem for fractional partial differential operators

Arran Fernandez
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Abstract

We present and prove a version of the elliptic regularity theorem for partial differential equations involving fractional Riemann-Liouville derivatives. In this case, regularity is defined in terms of Sobolev spaces $H^s(X)$: if the forcing of a linear elliptic fractional PDE is in one Sobolev space, then the solution is in the Sobolev space of increased order corresponding to the order of the derivatives. We also mention a few applications and potential extensions of this result.

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Arran Fernandez. 2018-04-03. An elliptic regularity theorem for fractional partial differential operators. https://doi.org/10.1007/s40314-018-0618-2

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