Properties of solutions of linear and quasilinear second-order equations with measurable coefficients which are neither strictly nor uniformly parabolic

In the cylinder Q_T=×(O,T], where is a bounded domain in Rⁿ, linear and quasilinear second-order equations with measurable coefficients in Q_T are considered which are, in general, neither strictly nor uniformly parablic. Previous results of the author for equations of this sort are developed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 69, pp. 45–64, 1977.