Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes
Articolo
Data di Pubblicazione:
2017
Citazione:
Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes / M. Cozzi. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 272:11(2017), pp. 4762-4837. [10.1016/j.jfa.2017.02.016]
Abstract:
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, reminiscent of that considered by E. De Giorgi in his seminal paper of 1957. The flexibility of these classes allows us to also establish regularity of solutions to rather general nonlinear integral equations.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Nonlocal energies; Nonlinear integral operators; Fractional De Giorgi classes; Holder continuity; Harnack inequality; Improved Caccioppoli inequality
Elenco autori:
M. Cozzi
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