Weak Harnack estimates for supersolutions to doubly degenerate parabolic equations

We establish weak Harnack inequalities for positive, weak supersolutions to certain doubly degenerate parabolic equations. The prototype of this kind of equations is $${\mathrm{\partial }}_{t}u-\mathrm{div}\mathrm{\mid }u{\mathrm{\mid }}^{m-1}\mathrm{\mid }Du{\mathrm{\mid }}^{p-2}Du=0,p>2,m+p>3.$$ Our proof is based on Caccioppoli inequalities, De Giorgi’s estimates and Moser’s iterative method.