On a new class of fractional partial differential equations

2014/03/31 by Shieh, Tien-Tsan, Spector, Daniel · 8 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1403.7942

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.

Cited by

• Fractional weighted Sobolev spaces associated to the Riesz fractional gradient
• Recovering functions via doubly homogeneous nonlocal gradients
• On blow-ups of sets with finite fractional variation
• A Lusin theorem for nonlocal gradients
• Riesz fractional gradient functionals defined on partitions: nonlocal-to-local variational limits
• A mixed formulation for the fractional Poisson problem
• A Survey on the Div-Curl Lemma and Some Extensions to Fractional Sobolev Spaces
• Local boundary conditions in nonlocal hyperelasticity via heterogeneous horizons

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