On some regularity and nonregularity results for solutions to parabolic systems

A short survey of recent results on smoothness of weak solutions to parabolic systems with nonsmooth coefficients in olane is given. Moreover, for space dimensions nge 3 and any closed subset F in R^n we construct a linear parabolic system with bounded measurable coefficients and its solution which is essentially discontinuous on F and essentially continuous on R^nF.