Fractional De Giorgi classes and applications to nonlocal regularity theory

Matteo Cozzi

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

6 Citations (SciVal)
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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

Funding

Acknowledgements The author wishes to thank Serena Dipierro, the Università degli Studi di Bari, and INdAM for their kind invitation, warm hospitality, and financial support. The author also thanks the anonymous referee for her/his keen comments on a previous version of this note. The author is supported by the “María de Maeztu” MINECO grant MDM-2014-0445, by the MINECO grant MTM2017-84214-C2-1-P, and by a Royal Society Newton International Fellowship.

Keywords

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

ASJC Scopus subject areas

  • General Mathematics

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