Inserted: 23 nov 2013
Last Updated: 3 jun 2014
Journal: Adv. Calc. Var.
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