Fractional De Giorgi Classes and Applications to Nonlocal Regularity Theory

  • Matteo CozziEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 33)


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 Nonlocal Caccioppoli inequality Hölder continuity Harnack inequality Nonlocal functionals Nonlinear integral operators 

2010 Mathematics Subject Classification

49N60 35B45 35B50 35B65 35R11 47G20 



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 “Mara de Maeztu” MINECO grant MDM-2014-0445, by the MINECO grant MTM2017-84214-C2-1-P, and by a Royal Society Newton International Fellowship.


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Authors and Affiliations

  1. 1.University of Bath, Department of Mathematical SciencesBathUK

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