Lipschitz continuity for energy integrals with variable exponents

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Regularity for scalar integrals without structure conditions (2018, background): “In this context see [10, 14, 25] and recently [13, 19, 20].”
Regularity results for vectorial minimizers of a class of degenerate convex integrals (2018, background): “[33], [42], [43] and, for other regularity results under a Sobolev type assumption with respect to the x-variable, see [18], [27], [28], [31]).”
A variational approach to parabolic equations under general and p,q-growth conditions (2020, background): “Among them there are variational integrands fulfilling a standard growth condition from below and above, functionals of non-standard p, q−growth and double phase (as in [4–6,23,24] and [21,29,34,35]), functionals with exponential growth (see [7,44,46]), variable exponents [21,26,33,36,37] and Orlicz”
Maximal regularity for local minimizers of non-autonomous functionals (2019, methodology): “Such functionals have been treated by Eleuteri–Marcellini–Mascolo [36, 37, 38].”