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Fundamental solutions of certain degenerate second-order parabolic equations. (English. Russian original) Zbl 0507.35045
Math. Notes 31, 283-289 (1982); translation from Mat. Zametki 31, 559-570 (1982).

MSC:
35K65 Degenerate parabolic equations
35K10 Second-order parabolic equations
35A08 Fundamental solutions to PDEs
Keywords:
construction
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References:
[1] A. N. Kolmogorov, ?Zufällige Bewegungen,? Ann. Math. (2),35, 116-117 (1934). · JFM 60.1159.01 · doi:10.2307/1968123
[2] I. M. Sonin, ?On a class of degenerate diffusion processes,? Teor. Veroyatn. Ee Primen.,12, No. 3, 540-547 (1967). · Zbl 0183.19901
[3] L. Hörmander, ?Hypoelliptic second-order differential equations,? Acta Math.,119, Nos. 3-4, 147-171 (1967). · Zbl 0156.10701 · doi:10.1007/BF02392081
[4] L. P. Kuptsov, ?On Harnack’s inequality for generalized solutions of second-order degenerate elliptic equations,? Differents. Uravn.,4, No. 1, 110-122 (1968).
[5] Ya. I. Shatyro, ?On the smoothness of the solutions of certain degenerate second-order equations,? Mat. Zametki,10, No. 1, 101-112 (1971).
[6] L. P. Kuptsov, ?On the fundamental solutions of a certain class of elliptic?parabolic second-order equations,? Differents. Uravn.8, No. 9, 1649-1660 (1972).
[7] L. P. Kuptsov, ?A mean value theorem and a maximum principle for a Kolmogorov equation,? Mat. Zametki,15, No. 3, 479-489 (1974).
[8] L. P. Kuptsov, ?A mean property and a maximum principle for second-order parabolic equations,? Dokl. Akad. Nauk SSSR,242, No. 3, 529-532 (1978). · Zbl 0436.35040
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