Journal
ADVANCES IN CALCULUS OF VARIATIONS
Volume 8, Issue 4, Pages 321-336Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/acv-2014-0009
Keywords
Fractional gradient; fractional Sobolev inequalities; fractional partial differential equations; Bessel potential spaces
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Funding
- National Science Council of Taiwan [NSC-101-2115-M-009-014-MY3]
- Technion Fellowship
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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.
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