On a new class of fractional partial differential equations

Tien Tsan Shieh, Eli Spector

Research output: Contribution to journalArticle

16 Scopus citations

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
StatePublished - 1 Oct 2015

Keywords

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

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