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A priori estimate for the derivative \(u_ x\) of a solution of a quasilinear parabolic equation. (Russian. English summary) Zbl 0558.35031

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
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