Quasilinear parabolic operators with discontinuous ingredients Original Research Article

Let View the MathML source, be a cylinder of height T>0 and C1,1-smooth base Ω. Unique strong solvability in the Sobolev spaces Wq2,1(Q), q>n+2 is proved for oblique derivative boundary value problem for quasilinear nondivergence form strictly parabolic equation with vanishing mean oscillation coefficients View the MathML source where aij and f are Carathéodoryʹs functions. An essential step of our investigations is deriving of suitable a priori estimates for the solution and its spatial gradient which makes possible the application of Leray–Schauderʹs fixed point theorem.