Fractional De Giorgi classes and applications to nonlocal regularity theory

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Abstract

We present some recent results obtained by the author on the regularity of solutions to nonlocal variational problems. In particular, we review the notion of fractional De Giorgi class, explain its role in nonlocal regularity theory, and propose some open questions in the subject.

Original languageEnglish
Title of host publicationContemporary Research in Elliptic PDEs and Related Topics
Place of PublicationCham, Switzerland
PublisherSpringer International Publishing
Pages277-299
Number of pages23
ISBN (Print)9783030189204
DOIs
Publication statusE-pub ahead of print - 13 Jul 2019

Publication series

NameSpringer INdAM (SINDHAMS) Series
Volume33
ISSN (Print)2281-518X

Keywords

  • Fractional De Giorgi classes
  • Harnack inequality
  • Hölder continuity
  • Nonlinear integral operators
  • Nonlocal caccioppoli inequality
  • Nonlocal functionals

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Cozzi, M. (2019). Fractional De Giorgi classes and applications to nonlocal regularity theory. In Contemporary Research in Elliptic PDEs and Related Topics (pp. 277-299). (Springer INdAM (SINDHAMS) Series; Vol. 33). Cham, Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-030-18921-1_7