Repository logo
 

An elliptic regularity theorem for fractional partial differential operators


Change log

Authors

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 Hs(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.

Description

Keywords

Fractional derivatives, Elliptic partial differential equations, Regularity theorems, Sobolev spaces

Journal Title

Computational and Applied Mathematics

Conference Name

Journal ISSN

2238-3603
1807-0302

Volume Title

37

Publisher

Springer Science and Business Media LLC
Sponsorship
EPSRC (1479943)