Higher integrability for nonlinear parabolic equations of <Emphasis Type="Italic">p</Emphasis>-Laplacian type

In this paper we give a new alternative proof of the local higher integrability in Orlicz spaces of the gradient for weak solutions of quasilinear parabolic equations of p-Laplacian type

$$\begin{array}{ll} u_t-\text{div} \left( \left | \nabla u\right|^{ p-2 } \nablau\right)=\text{div} \left(| \mathrm{ \bf f}|^{p-2} \mathrm{ \bf f}\right)\quad {\rm in}~\Omega\times (0,T] \end{array}$$

for any p > 0. Moreover, we point out that our results are homogeneousregularity estimates in Orlicz spaces and improve the known results for such equations by using some new techniques. Actually, our results can be extended to the global estimates and cover a more general class of degenerate/singular parabolic problems of p-Laplacian type.