Higher integrability for parabolic equations of $p(x,t)$-Laplacian type

By Stanislav N. Antontsev, V. Zhikov. Advances in Differential Equations, 2005

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Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “Further contributions to regularity, also for non-variational situations, and in the parabolic case, are those in [11, 118, 119, 59, 10, 17, 15, 16].”
Blowup in solutions of a quasilinear wave equation with variable‐exponent nonlinearities (2017, background): “More details on these problems can be found in previous studies.(22,23) In fact, only few work regarding hyperbolic problems with nonlinearities of variable-exponent type has appeared.”
Hölder estimates for parabolic p(x, t)-Laplacian systems (2012, background): “the scalar case N = 1 of (1), the higher integrability (4) was previously established by Antontsev and Zhikov [6].”
Overview of differential equations with non-standard growth (2010, background): “Antontsev and Zhikov [44] provide a Meyers type higher integrability result in a some sense more general setting, loosening the assumptions on p back to the log-Hölder condition.”
Calderón–Zygmund estimates for parabolic p(x,t)-Laplacian systems (2014, result): “This result was first established in the case of the p(x, t)-Laplacian equation by Antontsev and Zhikov [9], and later for a quite general class of parabolic systems with p(x, t)-growth independently by Zhikov and Pastukhova [34] and Bögelein and Duzaar [10].”