Un principe de maximum pour les solutions d'une classe d'inéquations paraboliques quasi-linéaires

Summary

In this paper we consider weak solutions of a class of variational inequalities associated with parabolic operators

$$\frac{{\partial u}}{{\partial t}} - \sum\limits_{j = 1}^N {D_j B_j (x,t,u,\nabla u) + B_0 (x,t,u,\nabla u)} $$

and we prove for them some L _∞ estimates in terms of the data and of the coefficients (cf. Theorem I and Theorem II). It will be shown as a particular case that the pointwise behavior of the solutions when t → ∞ is of exponential type.