Lorentz estimate with a variable power for parabolic obstacle problems with non-standard growths

We prove a global Lorentz estimate for the variable power of the gradients of weak solution to parabolic obstacle problems with p(t, x)-growth over a bounded nonsmooth domain. It is mainly assumed that the variable exponents p(t, x) satisfy a strong type log-Holder continuity, the associated nonlinearities are merely measurable in the time variable and have small BMO semi-norms in the spatial variables, while the underlying domain is quasiconvex. (C) 2018 Elsevier Inc. All rights reserved.