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
Cozzi, M. (2019). Fractional De Giorgi classes and applications to nonlocal regularity theory. In Contemporary Research in Elliptic PDEs and Related Topics (pp. 277-299). (Springer INdAM (SINDHAMS) Series; Vol. 33). Cham, Switzerland: Springer International Publishing. https://doi.org/10.1007/978-3-030-18921-1_7