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 in Book/Report/Conference proceeding › Chapter

2 Citations (SciVal)

24 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

@inbook{6ae9067d9a6140a3b6d8c385878a43cf,

title = "Fractional De Giorgi classes and applications to nonlocal regularity theory",

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.",

keywords = "Fractional De Giorgi classes, Harnack inequality, H{\"o}lder continuity, Nonlinear integral operators, Nonlocal caccioppoli inequality, Nonlocal functionals",

author = "Matteo Cozzi",

year = "2019",

month = jul,

day = "13",

doi = "10.1007/978-3-030-18921-1_7",

language = "English",

isbn = "9783030189204",

series = "Springer INdAM (SINDHAMS) Series",

publisher = "Springer International Publishing",

pages = "277--299",

booktitle = "Contemporary Research in Elliptic PDEs and Related Topics",

address = "Switzerland",

}

TY - CHAP

T1 - Fractional De Giorgi classes and applications to nonlocal regularity theory

AU - Cozzi, Matteo

PY - 2019/7/13

Y1 - 2019/7/13

N2 - 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.

AB - 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.

KW - Fractional De Giorgi classes

KW - Harnack inequality

KW - Hölder continuity

KW - Nonlinear integral operators

KW - Nonlocal caccioppoli inequality

KW - Nonlocal functionals

UR - http://www.scopus.com/inward/record.url?scp=85069794710&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-18921-1_7

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

M3 - Chapter

AN - SCOPUS:85069794710

SN - 9783030189204

T3 - Springer INdAM (SINDHAMS) Series

SP - 277

EP - 299

BT - Contemporary Research in Elliptic PDEs and Related Topics

PB - Springer International Publishing

CY - Cham, Switzerland

ER -

Fractional De Giorgi classes and applications to nonlocal regularity theory

Abstract

Publication series

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this