Fila, Marek A priori estimate for the derivative \(u_ x\) of a solution of a quasilinear parabolic equation. (Russian. English summary) Zbl 0558.35031 Acta Math. Univ. Comenianae 44-45, 251-256 (1984). We establish an a priori estimate for the derivative \(u_ x\) of a solution of the Cauchy problem for a quasilinear parabolic equation without any assumptions about the continuity of their coefficients. MSC: 35K55 Nonlinear parabolic equations 35K15 Initial value problems for second-order parabolic equations 35B45 A priori estimates in context of PDEs Keywords:a priori estimate; Cauchy problem; quasilinear parabolic equation PDFBibTeX XMLCite \textit{M. Fila}, Acta Math. Univ. Comenianae 44--45, 251--256 (1984; Zbl 0558.35031)