Regularity of Relaxed Minimizers of Quasiconvex Variational Integrals with (p, q)-growth

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On the Dirichlet problem for variational integrals in BV (2012, background): “Very similar degeneration phenomena have been studied in terms of Bernstein’s genre [13, 80] and in connection with (p, q)-growth conditions [57, 58, 59, 72, 33, 20, 34, 35, 60, 76, 77] and the L logL-energy [38, 63, 36].”
Non-autonomous functionals, borderline cases and related function classes (2016, background): “They have been the object of an intensive investigation during the last years, see for instance [8, 9, 11, 12, 13, 34, 43, 44, 54, 55].”
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, background): “More general quasiconvex functionals in the setting of (p, q)-growth conditions have been treated in [191,192].”
Parabolic equations with p, q-growth (2013, unknown): “[3,5,6,11,14,18,22,23] and the references therein.”
Regularity for Double Phase Variational Problems (2015, background): “The fundamentals of the corresponding regularity theory have been laid in Marcellini’s pioneering papers [35], [36], [37], [38]; further relevant contributions are for instance in [8], [9], [27], [28], [29], [30], [43], [44], [47].”