Literature Cited
R. Vyborny, “On properties of solutions of some boundary-value 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 equations and its applications,” Pac. J. Math.,8, 201–211 (1958).
L. I. Kamynin and B. N. Khimchenko, “The theorems of Giraud on the time derivative for a parabolic operator of second order,” Vestn. Mosk. Gos. Univ. Ser. Mat., Mekh., No. 5, 45–53 (1972).
L. I. Kamynin and B. N. Khimchenko, “On analogues of the theorem of Giraud type for a parabolic equation of second order,” Sib. Mat. Zh.,13, No. 4, 773–789 (1972).
L. I. Kamynin and B. N. Khimchenko, “Analogies of a Gireaux-type theorem for a second-order parabolic equation,” Sib. Mat. Zh.,14, No. 1, 86–110 (1973).
L. Nirenberg, “A strong maximum principle for parabolic equations,” Commun. Pure Appl. Math.,6, No. 2, 167–177 (1953).
C. Pucci, “Proprieta di massimo e minimo delle soluzioni di equazioni a derivate parziali del secondo ordine di tipo ellitico e parabolico,” Atti Acad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. e Natur.,23, No. 6, 370–375 (1957).
C. Pucci, Proprieta di massimo e minimo delle soluzioni di equazioni a derivate parziali del secondo ordine di tipo ellitico e parabolico. II,” Atti Acad. Naz. Lincei., Rend. Cl. Sci. Fis. Mat. e Natur.,24, No. 1, 3–6 (1958).
A. D. Aleksandrov, “Investigations on the maximum principle. I,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 126–157 (1958).
A. D. Aleksandrov, “Investigations on the maximum principle. II,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 3–15 (1959).
A. D. Aleksandrov, “Investigations on the maximum principle. III,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 16–32 (1959).
A. D. Aleksandrov, “Investigations on the maximum principle. IV,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 8–15 (1960).
A. D. Aleksandrov, “Investigations on the maximum principle. V,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 16–26 (1960).
L. I. Kamynin and B. N. Khimchenko, “Theorems of Giraud type for an equation of second order with a weakly degenerate nonnegative characteristic part,” Sib. Mat. Zh.,18, No. 1, 103–121 (1977).
O. A. Oleinik and E. V. Radkevich, Equations of Second Order with a Nonnegative Characteristic Form, Itogi Nauki. Matematicheskii Analiz, 1969, Nauka, Moscow (1971).
P. K. Rashevskii, “On the connectability of any two points of a completely nonholonomic space by an admissible line,” Uch. Zap. Pedagog. Inst. im. Libknekhta, Ser. Fiz., Mat.,2, 83–94 (1938).
L. I. Kamynin and B. N. Khimchenko, “On the strict extremum principle for degenerate parabolic equations of second order,” Dokl. Akad. Nauk SSSR,236, No. 5, 1060–1063 (1977).
S. M. Nikol'skii, A Course of Mathematical Analysis [in Russian], Vol. I, Nauka, Moscow (1973).
A. Friedman, Partial Differential Equations, Krieger (1976).
Additional information
Moscow State University, Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 21, No. 4, pp. 72–94, July–August, 1980.
Rights and permissions
About this article
Cite this article
Kamynin, L.I., Khimchenko, B.N. Theorems of Giraud type for second-order parabolic equations which admit degeneracy. Sib Math J 21, 535–551 (1980). https://doi.org/10.1007/BF00995954
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00995954