Regularity of the solution of the Cauchy problem for a higher-order parabolic equation

We prove the unique solvability of the Cauchy problem in a weighted Hölder space for a linear parabolic equation of order 2m under the condition that the lower coefficients and the right-hand side of the equation can have certain growth when approaching the plane that is the support of the initial data, while the higher coefficients do not necessarily satisfy the Dini condition near this plane.We construct a smoothness scale of solutions of the Cauchy problem in the corresponding weighted Hölder spaces.