Lp theory for fractional gradient PDE with VMO coefficients

Armin Schikorra, Tien Tsan Shieh, Daniel Eli Spector

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this paper, we prove L p estimates for the fractional derivatives of solutions to elliptic fractional partial differential equations whose coefficients are VMO. In particular, our work extends the optimal regularity known in the second order elliptic setting to a spectrum of fractional order elliptic equations.

Original languageEnglish
Pages (from-to)433-443
Number of pages11
JournalAtti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume26
Issue number4
DOIs
StatePublished - 1 Jan 2015

Keywords

  • Commutators
  • Fractional elliptic PDE
  • VMO coefficients

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