A weighted estimate of the gradient for nonnegative generalized solutions of quasilinear doubly degenerate parabolic equations

For nonnegative generalized solutions of doubly degenerate parabolic equations, a weighted estimate of the form, is establised.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 181, pp. 3–23, 1990.