A criterion for existence of L1-norms for higher-order derivatives of solutions to a homogeneous parabolic equation
Denis R. Akhmetov

The homogeneous Cauchy problem for general linear parabolic equation of second order with Holder continuous coefficients and uniformly continuous initial data was considered. It has been established that, in the class of initial data with a fixed continuity modulus, for existence of L1-norms for higher-order derivatives of bounded classical solutions to the problem it is necessary and sufficient for the continuity modulus to meet the Dini condition.