Higher differentiability results for solutions to a class of non-homogeneous elliptic problems under sub-quadratic growth conditions
| Autor: | Albert Clop, Andrea Gentile, Antonia Passarelli di Napoli |
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| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Bulletin of Mathematical Sciences, Vol 13, Iss 02 (2023) |
| Druh dokumentu: | article |
| ISSN: | 16643607 1664-3615 1664-3607 |
| DOI: | 10.1142/S166436072350008X |
| Popis: | We prove a sharp higher differentiability result for local minimizers of functionals of the form ℱ(w, Ω) =∫Ω[F(x,Dw(x)) − f(x) ⋅ w(x)]dx with non-autonomous integrand [Formula: see text] which is convex with respect to the gradient variable, under [Formula: see text]-growth conditions, with [Formula: see text]. The main novelty here is that the results are obtained assuming that the partial map [Formula: see text] has weak derivatives in some Lebesgue space [Formula: see text] and the datum [Formula: see text] is assumed to belong to a suitable Lebesgue space [Formula: see text]. We also prove that it is possible to weaken the assumption on the datum [Formula: see text] and on the map [Formula: see text], if the minimizers are assumed to be a priori bounded. |
| Databáze: | Directory of Open Access Journals |
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