Abstract
The paper considers a second-order linear parabolic equation whose coefficients satisfy a Dini condition. It is proven that the conditions for regularity of the boundary points for such an equation and for the heat-conduction equation coincide.
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E. M. Lankis, “Necessary and sufficient conditions for regularity of boundary points for the Dirichlet problem for the heat-conduction problem,” Dokl. Akad. Nauk SSSR,185, No. 3, 517–520 (1969).
A. A. Novruzov, “On certain criteria for regularity of boundary points for linear and quasilinear parabolic equations,” Dokl. Akad. Nauk SSSR,209, No. 4, 785–787 (1973).
I. T. Mamedov, “On sub- and super-solutions of a parabolic operator,” Uch. Zap. AzINEFTEKhIM, No. 6, 63–71 (1974).
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Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 717–723, November, 1976.
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Mamedov, I.T. Regularity of boundary points for linear equations of parabolic type. Mathematical Notes of the Academy of Sciences of the USSR 20, 961–965 (1976). https://doi.org/10.1007/BF01146919
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DOI: https://doi.org/10.1007/BF01146919