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 |
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| 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 |
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