Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes
| Autor: | Matteo Cozzi |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Class (set theory)
010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Hölder condition Extension (predicate logic) Term (logic) 01 natural sciences 010101 applied mathematics Sobolev space Mathematics - Analysis of PDEs Harnack's principle Bounded function FOS: Mathematics Applied mathematics 0101 mathematics 49N60 47G20 35R11 35D10 35B65 Analysis Analysis of PDEs (math.AP) Harnack's inequality Mathematics |
| Zdroj: | Journal of Functional Analysis. 272:4762-4837 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2017.02.016 |
| Popis: | 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, H\"older 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. Comment: 59 pages |
| Databáze: | OpenAIRE |
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