caa a22 4500 606194460 CHVBK 20210128100914.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00030-015-0324-3 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0324-3 Passarelli di Napoli Antonia Dipartimento di Matematica e Applicazioni "R. Caccioppoli”, Università di Napoli "Federico II”, Via Cintia, 80126, Napoli, Italy aut A $${C^{1,\alpha}}$$ C 1 , α partial regularity result for non-autonomous convex integrals with discontinuous coefficients [Elektronische Daten] [Antonia Passarelli di Napoli] We establish the $${C^{1,\alpha}}$$ C 1 , α partial regularity of vectorial minimizers of non autonomous convex integral functionals of the type $$\mathcal{F}(u;\,\Omega):=\int_{\Omega}f(x, Du)\, dx,$$ F ( u ; Ω ) : = ∫ Ω f ( x , D u ) d x , with p-growth into the gradient variable. As a novel feature, we allow discontinuous dependence on the x variable, through a suitable Sobolev function. The Hölder's continuity of the gradient of the minimizers is obtained outside a negligible set and this an unavoidable feature in the vectorial setting. Here, the so called singular set has to take into account also of the possible discontinuity of the coefficients. Springer Basel, 2015 Variational integrals nationallicence Discontinuous coefficients nationallicence Partial regularity nationallicence Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1319-1343 1021-9722 22:5<1319 2015 22 30 https://doi.org/10.1007/s00030-015-0324-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0324-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Passarelli di Napoli Antonia Dipartimento di Matematica e Applicazioni "R. Caccioppoli”, Università di Napoli "Federico II”, Via Cintia, 80126, Napoli, Italy aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1319-1343 1021-9722 22:5<1319 2015 22 30