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Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes

Autor
Cozzi, M.
Tipus d'activitat
Article en revista
Revista
Journal of functional analysis
Data de publicació
2017-06-01
Volum
272
Número
11
Pàgina inicial
4762
Pàgina final
4837
DOI
https://doi.org/10.1016/j.jfa.2017.02.016 Obrir en finestra nova
URL
http://www.sciencedirect.com/science/article/pii/S0022123617300770 Obrir en finestra nova
Resum
We study energy functionals obtained by adding a possibly discontinuous potential to an interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that minimizers of such non-differentiable functionals are locally bounded, Hölder continuous, and that they satisfy a suitable Harnack inequality. Hence, we provide an extension of celebrated results of M. Giaquinta and E. Giusti to the nonlocal setting. To do this, we introduce a particular class of fractional Sobolev functions, r...
Paraules clau
Fractional De Giorgi classes, Harnack inequality, Holder continuity, Improved Caccioppoli inequality, Nonlinear integral operators, Nonlocal energies
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants

  • Cozzi, Matteo  (autor)