Literature Cited
I. G. Petrovskii, “On the first boundary-value problem for the heat equation,” Composition Math.,1, No. 3, 383–419 (1935).
I. R. Cannon, “Regularity at the boundary for solutions of linear parabolic differential equations,” Ann. Scuola Norm. Super., Pisa, Sci. Fis. e. Mat.,19, No. 3, 415–427 (1965).
L. I. Kamynin, “The maximum principle and boundary α-estimates of the solution of the first boundary-value problem for a parabolic equation in a noncylindrical region,” Zh. Vychislit. Matem. i Mat. Fiz.,7, No. 3, 551–567 (1967).
L. I. Kamynin and B. N. Khimchenko, “Lipschitz boundary estimates for the solution of secondorder elliptic-parabolic equations,” Dokl. Akad. Nauk SSSR,212 No. 3, 544–547 (1973).
L. I. Kamynin and B. N. Khimchenko, “The maximum principle and Lipschitz boundary estimates for the solution of a second-order elliptic-parabolic equation,” Sibirsk. Matem. Zh.,15, No. 2, 343–367 (1974).
L. I. Kamynin and B. N. Khimchenko, “Some problems of the qualitative theory of elliptic-parabolic equations,” in: Theory of Cubature Formulas and Applications of Functional Analysis to Some Problems of Mathematical Physics, Nauka (1973), pp. 129–132.
L. I. Kamynin, “On the smoothness of thermal potentials. I,” Differents. Uravnen,1, No. 6, 799–839 (1965).
L. I. Kamynin and B. N. Khimchenko, “On analogs of Giraud's theorem for second-order parabolic equations,” Sibirsk. Matem. Zh.,14, No. 1, 86–110 (1973).
L. I. Kamynin and B. N. Khimchenko, “The maximum principle for a second-order parabolic equation,” Sibirsk. Matem. Zh.,13, No. 4, 773–789 (1972).
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Cliffs (1964).
L. I. Kamynin and B. N. Khimchenko, “The maximum principle and local regularity (in the Lipschitz sense) of the solutions of a second-order parabolic equation, near the lateral part of the parabolic boundary,” Dokl. Akad. Nauk SSSR,219, No. 4, 785–788 (1974).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 16, No. 6, pp. 1172–1187, November–December, 1975.
Rights and permissions
About this article
Cite this article
Kamynin, L.I., Khimchenko, B.N. The maximum principle and local Lipschitz estimates near the lateral boundary for solutions of second-order parabolic equations. Sib Math J 16, 897–909 (1975). https://doi.org/10.1007/BF00967385
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00967385