Fractional De Giorgi classes and applications to nonlocal regularity theory

Matteo Cozzi

Research output: Chapter or section in a book/report/conference proceedingChapter or section

5 Citations (SciVal)
40 Downloads (Pure)


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
Number of pages23
ISBN (Print)9783030189204
Publication statusE-pub ahead of print - 13 Jul 2019

Publication series

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


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

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'Fractional De Giorgi classes and applications to nonlocal regularity theory'. Together they form a unique fingerprint.

Cite this