On a new class of fractional partial differential equations
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Tien-Tsan Shieh
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Daniel E. Spector
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.
Funding source: National Science Council of Taiwan
Award Identifier / Grant number: NSC-101-2115-M-009-014-MY3
Funding source: Technion
Award Identifier / Grant number: Fellowship
The first author would like to thank Professor Ming-Chih Lai for his support in doing this project. The second author would like to thank Itai Shafrir, Lorena Aguirre, Rahul Garg, Georgios Psaradakis and Baptiste Devyver for their insightful discussions during the preparation of this paper, as well as the CMMSC at National Chiao Tung University for its support during the undertaking of this research.
© 2015 by De Gruyter
