An elliptic regularity theorem for fractional partial differential operators

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.

10 pages, 1 figure; accepted for publication in Computational & Applied Mathematics

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Cited by in corpus (1)

• Solving PDEs of fractional order using the unified transform method