Fractional De Giorgi classes and applications to nonlocal regularity theory

Matteo Cozzi

doi:10.1007/978-3-030-18921-1_7

Fractional De Giorgi classes and applications to nonlocal regularity theory

Matteo Cozzi

Department of Mathematical Sciences

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

2 Citations (SciVal)

28 Downloads (Pure)

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 language	English
Title of host publication	Contemporary Research in Elliptic PDEs and Related Topics
Place of Publication	Cham, Switzerland
Publisher	Springer International Publishing
Pages	277-299
Number of pages	23
ISBN (Print)	9783030189204
DOIs	https://doi.org/10.1007/978-3-030-18921-1_7
Publication status	E-pub ahead of print - 13 Jul 2019

Publication series

Name	Springer INdAM (SINDHAMS) Series
Volume	33
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)

Access to Document

10.1007/978-3-030-18921-1_7

proceedingBariRev.PDF
This is a post-peer-review, pre-copyedit version of an article published in Contemporary Research in Elliptic PDEs and Related Topics. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-18921-1_7
Accepted author manuscript, 421 KB

Cite this

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KW - Harnack inequality

KW - Hölder continuity

KW - Nonlinear integral operators

KW - Nonlocal caccioppoli inequality

KW - Nonlocal functionals

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Fractional De Giorgi classes and applications to nonlocal regularity theory

Abstract

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Keywords

ASJC Scopus subject areas

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