Summary of Research
of Denis R. Akhmetov

My research, which is resulted in the series of papers published in 1998-2000 years, is concentrated in the investigation of properties of classical solutions to the Cauchy problem for a general linear, uniformly parabolic operator of second order. There were considered conditions on the continuity moduli of the coefficients and the right-hand side of the equation which guarantee existence of a classical solution and an exact coercive estimate for the one that is similar to the well-known Schauder-type estimate for arbitrary solution in a Holder class of functions. The one of the main goals of my investigation was to generalize the Schauder-type estimate in the case of arbitrary continuity modulus, rather than the Holder condition only.