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Literature Cited
G. Giraud, “Généralisation des problémes sur les opérations du type elliptiques,” Bull. Sci. Math.,60, 316–352 (1932).
G. Giraud, “Problémes des valeurs à la frontiére relatifs à certaines don ées discontinues,” Bull. Soc. Math. France61, 1–54 (1933).
O. A. Oleinik, “On the properties of the solutions of some boundary problems for equations of elliptic type,” Mat. Sb.,30, No. 3, 695–702 (1952).
E. Hopf, “A remark on linear differential equation of the second order,” Proc. Am. Math. Soc.,3, 791–793 (1952).
R. Vyborny, “On the properties of the solutions of some boundary problems for equations of parabolic type,” Dokl. Akad. Nauk SSSR,117, No. 3, 563–565 (1957).
A. Friedman, “Remarks on the maximum principle for parabolic equation and its application,” Pac. J. Math.,8, 201–211 (1958).
L. I. Kamynin and B. N. Khimchenko, “On the maximum principle for second-order parabolic equations,” Dokl. Akad. Nauk SSSR,200, No. 2, 282–285 (1971).
L. I. Kamynin and B. N. Khimchenko, “Pn the maximum principle for a second-order elliptic-parabolic equations,” Sib. Mat. Zh.,13, No. 4, 773–789 (1972).
L. I. Kamynin and B. N. Khimchenko, “On the applications of the maximum principle to second-order parabolic equations,” Dokl. Akad. Nauk SSSR,204, No. 3, 529–532 (1972).
L. I. Kamynin and B. N. Khimchenko, “Analogs of the Giraud theorem for a second-order parabolic equations,” Sib. Mat. Zh.,14, No. 1, 86–110 (1973).
L. I. Kamynin and B. N. Khimchenko, “On theorems of Giraud type for a second-order elliptic operator which becomes weakly degenerate near the boundary,” Dokl. Akad. Nauk SSSR,224, No. 4, 752–755 (1975).
O. A. Oleinik and E. V. Radkevich, “Second-order equations with nonnegative characteristic form,” Mat. Analiz, No. 1, Izd-vo VINITI, Moscow (1971).
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall (1964).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 18, No. 1, pp. 103–121, January–February, 1977.
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Kamynin, L.I., Khimchenko, B.N. Theorems of the Giraud type for second-order equations with weakly degenerate nonnegative characteristic part. Sib Math J 18, 76–91 (1977). https://doi.org/10.1007/BF00966952
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DOI: https://doi.org/10.1007/BF00966952