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Mean value theorem and a maximum principle for Kolmogorov’s equation. (English. Russian original) Zbl 0333.35040
Math. Notes 15, 280-286 (1974); translation from Mat. Zametki 15, 479-489 (1974).

MSC:
35K10 Second-order parabolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35E05 Fundamental solutions to PDEs and systems of PDEs with constant coefficients
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[1] A. N. Kolmogorov, ?Zufallige Bewegungen,? Ann. of Math.,2, No. 35, 116-117 (1934). · Zbl 0008.39906 · doi:10.2307/1968123
[2] B. Pini, ?Maggioranti e minoranti delle soluzioni delle equazioni paraboliche,? Ann. Mat. Pura Appl., 37, 249-264 (1954). · Zbl 0057.32703 · doi:10.1007/BF02415101
[3] W. Fulks, ?A mean value theorem for the heat equation,? Proc. Amer. Math. Soc.,17, No. 1, 6-11 (1966). · Zbl 0152.10503 · doi:10.1090/S0002-9939-1966-0192200-3
[4] L. Nirenberg, ?A strong maximum principle for parabolic equations,? Comm. Pure Appl. Math.,6, 167-177 (1953). · Zbl 0050.09601 · doi:10.1002/cpa.3160060202
[5] M. Weber, ?The fundamental solutions of a degenerate partial differential equation of parabolic type,? Trans. Amer. Math. Soc.,71, 24-37 (1951). · Zbl 0043.09901 · doi:10.1090/S0002-9947-1951-0042035-0
[6] A. M. Il’in, ?On a class of ultraparabolic equations,? Dokl. Akad. Nauk SSSR,159, 1214-1217 (1964).
[7] L. Hörmander, ?Hypoelliptic differential equations of the second order,? Acta Math.,119, 147-171 (1967). · Zbl 0156.10701 · doi:10.1007/BF02392081
[8] P. R. Halmos, Finite Dimensional Vector Spaces, Annals of Math. Studies, Vol. No. 7, Princeton Univ. Press, Princeton (1942). · Zbl 0107.01404
[9] Ya. I. Shatyro, ?On the smoothness of the solutions of some degenerate second-order equations,? Matem. Zametki,10, No. 1, 101-111 (1971).
[10] L. P. Kuptsov, ?On the fundamental solutions of a class of second-order elliptic-parabolic equations,? Differents. Uravnen.,8, No. 9, 1649-1660 (1972).
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