Reverse Hölder inequalities in parabolic problems with anisotropic data spaces (Q1920143)

The author gives the generalization of her former results: Reverse inequalities contain additional terms in the space \(L_{m,r}\) (summability to the power \(m\) with respect to spatial variables and to the power \(r\) with respect to the time variable). This is a convenient tool for considering parabolic systems. The reverse inequalities with anisotropic additional terms are deduced for gradients of generalized solutions to quasilinear parabolic problems with non-smooth conditions imposed on the conormal derivative. It is proved that the summability of the gradients of solutions can be increased.