We study the smoothness of a solution to the Cauchy problem for a one-dimensional parabolic equation with Dini–continuous coefficients in the Dini space. We obtain estimates for the volume parabolic potential and its spatial first order derivative in the Dini space.
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Translated from Problemy Matematicheskogo Analiza 112, 2021, pp. 57-69.
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Zhenyakova, I.V., Cherepova, M.F. Regularity of Solution to the Cauchy Problem for Parabolic Equation in the Dini Space. J Math Sci 259, 172–186 (2021). https://doi.org/10.1007/s10958-021-05609-7
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DOI: https://doi.org/10.1007/s10958-021-05609-7