Calculus of Variations and Geometric Measure Theory
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T. T. Shieh - D. Spector

On a new class of fractional partial differential equations

created by spector on 23 Nov 2013
modified on 03 Jun 2014

[BibTeX]

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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