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Margaryan, V. N.; Ghazaryan, H. G.

On relationships between different concepts of hypoellipticity. (English) Zbl 1532.35132

J. Math. Sci., New York 271, No. 5, Series A, 658-665 (2023).
Summary: The paper investigates connections and relations between different types (concepts) of hypoelliptic differential operators (symbols (characteristic polynomials) of these operators).

MSC:

35H10 Hypoelliptic equations
26D05 Inequalities for trigonometric functions and polynomials
35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals

Keywords:

hypoelliptic according to Hörmander operator (polynomial); partially hypoelliptic according to Gȧrding-Malgrange; according to Elliot and according to Burenkov operator (polynomial); Newton’s polyhedron
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References:

[1] L. Hörmander, The Analysis of linear Partial Differential Operators. v. 2. Springer-Verlag (1983). · Zbl 0521.35002
[2] Malgrange, B., Sur une class d’operateurs differenciels hypoelliptiques, Bull. Math. France, 85, 283-306 (1957) · Zbl 0082.09303 · doi:10.24033/bsmf.1490
[3] L. Gȧrding, B. Malgrange, Operateurs differentiels partillement hypoelliptiques et partillement elliptiques. Math. Scand. 9, 5 - 21, (1961). · Zbl 0108.10101
[4] Elliott, RJ, Almost hypoelliptic differential operators, Proc. of the London math. Soc., 53-19, 3, 537-552 (1969) · Zbl 0172.38101 · doi:10.1112/plms/s3-19.3.537
[5] Kazaryan, GG; Margaryan, VN, Support of the hypoellipticity of linear differential operators, Izw. AN Arm. SSR, 21, 5, 453-470 (1986) · Zbl 0619.35020
[6] V.I. Burenkov, An analogue of L. Hörmander’s hypoellipticity theorem for functions tending to zero at infinity. Collection of reports of the 7th Soviet - Czechoslovak seminar. Yerevan, 63 - 67, 1982.
[7] A.G. khovanskii, Newton Polyhedra (algebra and geometry), Amer. Math. Soc.Transl., vol. 153, no 2, 1 - 15, 1992.
[8] Mikhailov, VP, Behavior at infinity of a certain class of polynomials, Proc. Steklov Inst. Math., 91, 59-81 (1967) · Zbl 0185.33901
[9] G.G. Kazaryan, On almost hypoelliptic polynomials increasing at infinity. Izw. NAN Arm., Math. vol. 46, no. 6, 11 30, 2011. · Zbl 1302.35122
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