On the Smoothness of the Solutionto the Cauchy Problem for a Parabolic Equationwith Dini-Continuous Coefficients

We consider the Cauchy problem for a spatially multidimensional second-order parabolic equation with Dini-continuous coefficients. The initial function belongs to the class of continuous and bounded functions with uniformly continuous and bounded first-order spatial derivatives. The right-hand side of the equation can grow in a certain way when approaching the plane of the initial data. The smoothness of the solution to this problem is investigated and estimates of the solution and its first-order spatial derivatives are obtained using the Poisson potential and the volume potential.