On a new class of partial differential equations

Daniel Spector National Chiao Tung University Tien-Tsan Shieh National Central University

Analysis of PDEs mathscidoc:1703.03003

Adv. Calc. Var. 8 , 8, (4), 321–336. , 2015
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 to many classical results in the Sobolev spaces to the nonlocal and fractional setting in a natural way.
Fractional Gradient, Fractional Sobolev Inequalities, Fractional Partial Differential Equations, Bessel Potential Spaces.
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  title={On a new class of partial differential equations},
  author={Daniel Spector, and Tien-Tsan Shieh},
  booktitle={Adv. Calc. Var. 8 },
  pages={321–336. },
Daniel Spector, and Tien-Tsan Shieh. On a new class of partial differential equations. 2015. Vol. 8. In Adv. Calc. Var. 8 . pp.321–336. . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170309063554038969625.
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