Ultraparabolic equations with degeneration

We prove existence and uniqueness theorems for regular solutions to boundary value problems for ultraparabolic differential equations with temporal variables \(y_1,...,y_m\) $y_1,...,y_m$ and spatial variables \(x_1,...,x_n\) $x_1,...,x_n$ . The problems under study have the peculiarity that the corresponding differential equations may degenerate both in the temporal and spatial parts; moreover, the evolution direction with respect to some temporal variables can change arbitrarily.