Global L^r -estimates and regularizing effect for solutions to the p(t,x)-Laplacian systems

We consider the initial boundary value problem for the p(t,x)-Laplacian system in a bounded domain. If the initial data belongs to L^{r_0}, r_0≥2, we prove a global L^{r_0}-regularity result uniformly in t>0 that, in the particular case r_0=infty, gives a maximum modulus theorem. Under the assumption p−=inf p(t,x)>2n/(n+r_0), we also study L^{r_0}−L^r estimates for the solution, for r≥r_0.