Abstract
We study the regularity properties of local minimizers of non-autonomous convex integral functionals of the type
when the integrand f has almost linear growth with respect to the gradient variable and the dependence on the x-variable is controlled by a function which belongs to a suitable Orlicz Sobolev space.
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The author has been supported by the Gruppo Nazionale per l’ Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM), by Project Legge 5/2007 Regione Campania “Spazi pesati ed applicazioni al calcolo delle variazioni” and by “Programma triennale della Ricerca dell’Università degli Studi di Napoli “Parthenope”—Sostegno alla ricerca individuale 2015-2017”.
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Giova, R. Regularity results for non-autonomous functionals with \(\varvec{{L}\log {L}}\)-growth and Orlicz Sobolev coefficients. Nonlinear Differ. Equ. Appl. 23, 64 (2016). https://doi.org/10.1007/s00030-016-0419-5
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DOI: https://doi.org/10.1007/s00030-016-0419-5