×

Subellipticity of integro-differential operators verifying the maximum principle. (Sous-ellipticité d’opérateurs intégro-différentiels vérifiant le principe du maximum.) (French) Zbl 0788.45007

The authors extend to pseudo-differential operators of the type \(\Sigma X_ j^*X_ j\), with \(X_ j\) of order \(\leq 1\), some known results on the subellipticity of second order operators.
Reviewer: I.Vrabie (Iaşi)

MSC:

45K05 Integro-partial differential equations
35S05 Pseudodifferential operators as generalizations of partial differential operators
PDFBibTeX XMLCite
Full Text: Numdam EuDML

References:

[1] P. Bolley - J. Camus - J. Nourrigat , La condition de Hörmander-Kohn pour les opérateurs pseudo-différentiels , Comm. Partial Differential Equations , 7 ( 2 ) ( 1982 ), 197 - 221 . MR 646136 | Zbl 0497.35086 · Zbl 0497.35086
[2] J.-M. Bony - P. Courrège - P. Priouret , Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum , Ann. Inst. Fourier , Grenoble , 18 , 2 ( 1968 ), 369 - 521 . Numdam | MR 245085 | Zbl 0181.11704 · Zbl 0181.11704
[3] C.E. Cancelier , Problèmes aux limites pseudo-différentiels donnant lieu au principe du maximum , Comm. Partial Differential Equations , 11 ( 15 ) ( 1986 ), 1677 - 1726 . MR 871109 | Zbl 0646.35080 · Zbl 0646.35080
[4] F. Gimbert - P.L. Lions , Existence and regularity results for solutions of second order, elliptic, integro-differential operators , Ricerche Mat. , vol. XXXIII , 2 ( 1984 ). MR 810193 | Zbl 0579.45010 · Zbl 0579.45010
[5] L. Hörmander , Hypoelliptic second order differential equations , Acta Math. 119 ( 1967 ), 147 - 171 . MR 222474 | Zbl 0156.10701 · Zbl 0156.10701
[6] L. Hörmander , The analysis of linear partial differential operators IV , Springer-Verlag , 1985 . MR 781537 | Zbl 0612.35001 · Zbl 0612.35001
[7] J.J. Kohn , Pseudo-differential operators and non-elliptic problems, Pseudo differential operators ( C.I.M.E. Stresa , 1968 ), Edizioni Cremonese , Rome , 1969 , 157 - 165 MR 41 # 3972. MR 259334
[8] H. Kumano-Go , A calculus of Fourier integral operators on Rn and the fundamental solution for an operator of hyperbolic type , Comm. Partial Differential Equations , 1 ( 1 ) ( 1976 ), 1 - 44 . MR 397482 | Zbl 0331.42012 · Zbl 0331.42012
[9] J.L. Lions - J. Peetre , Sur une classe d’espaces d’interpolation . Institut des Hautes Etudes Scientifiques, Publications mathématiques n^\circ 19 , 1964 . Numdam | Zbl 0148.11403 · Zbl 0148.11403
[10] R. Mikulevicius - H. Pragarauskas , On the existence and uniqueness of solutions to the martingal problem , à paraître. · Zbl 1296.45009
[11] J. Nourrigat , Subelliptic estimates for systems of pseudo-differential operators . Notas de curso , Instituto de Matemática, Universidad federal de Pernambuco , Recife 1982 .
[12] O.A. Oleinik - E.V. Radkevic , Second order equations with nonnegative characteristic form , Amer. Math. Soc. , Providence, Rhode Island , Plenum Press , 1973 . MR 457908
[13] J.P. Serre , Lectures given at Harvard University, Lie algebras and Lie groups , W.A. Benjamin, Inc. New-York Amsterdam , 1965 . MR 218496 | Zbl 0132.27803 · Zbl 0132.27803
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.