Baroni, P.; Colombo, M.; Mingione, G. Non-autonomous functionals, borderline cases and related function classes. (English) Zbl 1335.49057 St. Petersbg. Math. J. 27, No. 3, 347-379 (2016) and Algebra Anal. 27, No. 3, 6-50 (2015). Summary: The class of non-autonomous functionals under study is characterized by the fact that the energy density changes its ellipticity and growth properties according to the point; some regularity results are proved for related minimizers. These results are the borderline counterpart of analogous ones previously derived for non-autonomous functionals with \((p,q)\)-growth. Also, similar functionals related to Musielak-Orlicz spaces are discussed, in which basic properties like the density of smooth functions, the boundedness of maximal and integral operators, and the validity of Sobolev-type inequalities are naturally related to the assumptions needed to prove the regularity of minima. Cited in 266 Documents MSC: 49N60 Regularity of solutions in optimal control 49J10 Existence theories for free problems in two or more independent variables 35J20 Variational methods for second-order elliptic equations 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 42B25 Maximal functions, Littlewood-Paley theory Keywords:non-autonomous functionals; nonstandard growth; minimizers; Hölder regularity; Musielak-Orlicz spaces; maximal operators; Sobolev-type inequalities × Cite Format Result Cite Review PDF Full Text: DOI References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.