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.
Fractional De Giorgi classes and applications to nonlocal regularity theory / M. Cozzi (SPRINGER INDAM SERIES). - In: Contemporary Research in Elliptic PDEs and Related Topics / [a cura di] S. Dipierro. - [s.l] : Springer International Publishing, 2019. - ISBN 9783030189204. - pp. 277-299 [10.1007/978-3-030-18921-1_7]
Fractional De Giorgi classes and applications to nonlocal regularity theory
M. Cozzi
2019
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.
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