On a new class of fractional partial differential equations

Tien Tsan Shieh, Daniel E. Spector

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)321-336
Number of pages16
JournalAdvances in Calculus of Variations
Volume8
Issue number4
DOIs
Publication statusPublished - 2015 Oct 1
Externally publishedYes

Keywords

  • Bessel potential spaces
  • Fractional gradient
  • fractional Sobolev inequalities
  • fractional partial differential equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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