Harnack's inequality for doubly nonlinear equations of slow diffusion type.

In this article we prove a Harnack inequality for non-negative weak solutions to doubly nonlinear parabolic equations of the form ∂ t u - div A ( x , t , u , D u m ) = div F , where the vector field A fulfills p-ellipticity and growth conditions. We treat the slow diffusion case in its full range, i.e. all exponents m > 0 and p > 1 with m ( p - 1 ) > 1 are included in our considerations.