  We consider the initial boundary value problem for the p(t, x)-Laplacian
system in a bounded domain \Omega. If the initial data belongs to L^{r_0}, r_0
\geq 2, we give a global L^{r_0}({\Omega})-regularity result uniformly in t>0
that, in the particular case r_0 =\infty, implies a maximum modulus theorem.
Under the assumption p- = \inf p(t, x) > 2n/(n+r_0), we also state L^{r_0}- L^r
estimates for the solution, for r \geq r_0. Complete proofs of the results
presented here are given in the paper [F. Crispo, P. Maremonti, M. Ruzicka,
Global L^r-estimates and regularizing effect for solutions to the p(t, x)
-Laplacian systems, accepted for publication on Advances in Differential
Equations, 2017].
