Accepted Paper

Inserted: 23 nov 2013
Last Updated: 3 jun 2014

Journal: Adv. Calc. Var.
Year: 2013

Abstract:

In this paper, we study a new class of fractional partial differential equations which are obtained by minimizing variational problems in fractional Sobolev spaces. We introduce a notion of fractional gradient which has the potential to extend many classical results in the Sobolev spaces to the nonlocal and fractional setting in a natural way.

Keywords: Fractional Gradient, Fractional Sobolev Spaces, Fractional PDE, Bessel Potential Spaces

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• Shieh-Spector-NCTS_Taipei-preprint.pdf