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 | |
| 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)
Cite this
Fractional De Giorgi classes and applications to nonlocal regularity theory. / Cozzi, Matteo.
Contemporary Research in Elliptic PDEs and Related Topics. Cham, Switzerland : Springer International Publishing, 2019. p. 277-299 (Springer INdAM (SINDHAMS) Series; Vol. 33).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
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
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 -