Regularity of solutions of boundary value problems for a second-order parabolic equation in weighted Hölder spaces

We consider the first boundary value problem and the oblique derivative problem for a linear second-order parabolic equation in noncylindrical not necessarily bounded domains with nonsmooth (with respect to t) and noncompact lateral boundary under the assumption that the right-hand side and the lower-order coefficients of the equation may have certain growth when approaching the parabolic boundary of the domain and all coefficients are locally Hölder with given characteristics of the Hölder property. We construct a smoothness scale of solutions of these boundary value problems in Hölder spaces of functions that admit growth of higher derivatives near the parabolic boundary of the domain.