On the maximum principle for doubly nonlinear parabolic equations

For a general class of doubly nonlinear parabolic equations, some versions of the maximum principle are established. They play an important role in studying the regularity of generalized solutions of such equations. In particular, the results obtained can be used in studying equations of the form $$frac{{partial u}}{{partial t}} - div{ |u|^l |nabla u} = 0, m > 1, l > 1 - m.$$ which have numerous applications in the mechanics of continuous media. Bibliography: 17 tiles.