We construct the fundamental solution to a multi-dimensional parabolic equations with Dini-continuous coefficients and obtain estimates for the solution. We show that the classical solution to the Cauchy problem for a parabolic equation with an unbounded right-hand side is smooth in the Dini space.
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Translated from Problemy Matematicheskogo Analiza 116, 2022, pp. 85-103.
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Zhenyakova, I.V., Cherepova, M.F. The Cauchy Problem for a Multi-Dimensional Parabolic Equation with Dini-Continuous Coefficients. J Math Sci 264, 581–602 (2022). https://doi.org/10.1007/s10958-022-06018-0
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DOI: https://doi.org/10.1007/s10958-022-06018-0