Conormal problem of higher-order parabolic systems with time irregular coefficients (Q2796097)

The interesting paper under review deals with \(L^p\) and Schauder estimates for higher-order divergence-type parabolic systems with discontinuous coefficients on a half-space and cylindrical domains with the conormal derivative boundary conditions. For the study of \(L^p\) estimates, the authors suppose that the principal coefficients are only bounded and measurable in the time variable \(t\) and have vanishing mean oscillations (VMO) with respect to the spatial variables \(x\). Schauder estimates are also obtained in two situations: the coefficients are Hölder continuous only in the \(x\) variables and the coefficients are Hölder continuous in the \(t\) variable and also on the lateral boundary.