La sous-ellipticité pour le problème $\bar{\partial }$-Neumann dans un domaine pseudoconvexe de $C^n$

La sous-ellipticité pour le problème

\bar{\partial}

-Neumann dans un domaine pseudoconvexe de

C^{n}

Derridj, Makhlouf

Séminaire Bourbaki : volume 1994/95, exposés 790-804, Astérisque, no. 237 (1996), Exposé no. 790, 21 p.

EuDML Zbl

@incollection{SB_1994-1995__37__7_0,
     author = {Derridj, Makhlouf},
     title = {La sous-ellipticit\'e pour le probl\`eme $\bar{\partial }${-Neumann} dans un domaine pseudoconvexe de $C^n$},
     booktitle = {S\'eminaire Bourbaki : volume 1994/95, expos\'es 790-804},
     series = {Ast\'erisque},
     note = {talk:790},
     pages = {7--27},
     year = {1996},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {237},
     zbl = {0874.35028},
     language = {fr},
     url = {https://www.numdam.org/item/SB_1994-1995__37__7_0/}
}

TY  - CHAP
AU  - Derridj, Makhlouf
TI  - La sous-ellipticité pour le problème $\bar{\partial }$-Neumann dans un domaine pseudoconvexe de $C^n$
BT  - Séminaire Bourbaki : volume 1994/95, exposés 790-804
AU  - Collectif
T3  - Astérisque
N1  - talk:790
PY  - 1996
SP  - 7
EP  - 27
IS  - 237
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/SB_1994-1995__37__7_0/
LA  - fr
ID  - SB_1994-1995__37__7_0
ER  -

%0 Book Section
%A Derridj, Makhlouf
%T La sous-ellipticité pour le problème $\bar{\partial }$-Neumann dans un domaine pseudoconvexe de $C^n$
%B Séminaire Bourbaki : volume 1994/95, exposés 790-804
%A Collectif
%S Astérisque
%Z talk:790
%D 1996
%P 7-27
%N 237
%I Société mathématique de France
%U https://www.numdam.org/item/SB_1994-1995__37__7_0/
%G fr
%F SB_1994-1995__37__7_0

Derridj, Makhlouf. La sous-ellipticité pour le problème $\bar{\partial }$-Neumann dans un domaine pseudoconvexe de $C^n$, dans Séminaire Bourbaki : volume 1994/95, exposés 790-804, Astérisque, no. 237 (1996), Exposé no. 790, 21 p.. https://www.numdam.org/item/SB_1994-1995__37__7_0/

Bibliographie
Cité par

[1] A Andreotti and E Vesentini - Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Htes Ét. Sc. Publ. Math., Vol. 24-25. | Numdam | Zbl | EuDML

[2] M. S. Baouendi and F. Trèves - About the holomorphic extension of C.R. functions on real hypersurfaces in complex space, Duke Math. J. 51 (1984), 77-107. | Zbl | MR

[3] S. Bell and E. Ligocka - A simplification and extension of Fefferman's theorem on biholomorphic mappings, Invent. Math. 57 (1980), 283-289. | Zbl | MR | EuDML | DOI

[4] T. Bloom - On the contact between complex manifolds and real hypersurfaces in $𝐂^{3}$ , Trans. A.M.S. 263 (1981), 515-529. | Zbl | MR

[5] T. Bloom and I. Graham - A geometric characterization of points of type $m$ on real submanifolds of $𝐂^{n}$ , J. of Diff. Geom. 12 (1977), 171-182. | Zbl | MR | DOI

[6] H. Boas and E. Straube - Sobolev estimates for the $\bar{\partial}$ -Neumann operator on domains in $𝐂^{n}$ admitting a defining function that is plurisubharmonic on the boundary, Math. Z. 206 (1991), 81-88. | Zbl | EuDML | DOI

[7] H. Boas and E. Straube - On equality of line type and variety type of real hypersurfaces in $𝐂^{n}$ , J. of Geom. Anal., Vol. n° 2 (1992), 95-98. | Zbl | MR | DOI

[8] D. Catlin - Necessary conditions for subellipticity of the $\bar{\partial}$ -Neumann problem, Annals of Math. 117 (1983), 147-171. | Zbl

[9] D. Catlin - Global regularity of the $\bar{\partial}$ -Neumann problem, Proc. Symp. Pure Math. Vol. 41 (1984). | Zbl | DOI

[10] D. Catlin - Boundary invariants of pseudoconvex domains Annals of Math. 120 (1984), 529-586. | Zbl | MR | DOI

[11] D. Catlin - Subelliptic estimates for the $\bar{\partial}$ -Neumann problem on pseudoconvex domains, Annals of Maths. 126 (1987), 131-191. | Zbl | DOI

[12] D. Catlin - Examples of sharp subelliptic estimates for the $\bar{\partial}$ -Neumann problem, non publié.

[13] D. C. Chang, A. Nagel and E. Stein - Estimates for the $\bar{\partial}$ -Neumann problem in pseudoconvex domains of finite type in $𝐂^{2}$ , Acta Math. 169 (1992), 153-228. | Zbl | DOI

[14] J.D'Angelo - Subelliptic estimates and failure of semi-continuity of orders of contact Annals of Math. 47 (1980), 955-957. | Zbl | MR

[15] J.D'Angelo - Real hypersurfaces, orders of contact and applications, Annals of Math. 115 (1982), 615-637. | Zbl | MR | DOI

[16] J.-P. Demailly - Estimations $L^{2}$ pour l'opérateur $\bar{\partial}$ d'un fibré vectoriel holomorphe, semi-positif, au-dessus d'une variété kählérienne complète, Ann. Sc. Ec. Norm. Sup 15 (1982), 457-511. | Numdam | Zbl | EuDML | DOI

[17] M. Derridj - Régularité pour $\bar{\partial}$ dans quelques domaines pseudoconvexes, J. of Diff. Geom. 13 n° 4 (1978), 559-576. | Zbl | DOI

[18] M. Derridj - Inégalités a priori et estimation sous-elliptique pour $\bar{\partial}$ dans des ouverts non pseudoconvexes, Math. Ann. (1980), 27-48. | Zbl | EuDML | DOI

[19] K. Diederich and J. E. Fornaess - Pseudoconvex domains with real analytic boundary, Ann. of Math. 107 (1978), 371-384. | Zbl | MR | DOI

[20] K. Diederich and G. Herbort - Geometric and analytic invariants on pseudoconvex domains. Comparison results, preprint. | Zbl | DOI

[21] Y. Egorov - Subelliptic operators, Usp. Math. Nauk. 30 (n° 3), 57-104, English transl. Russ. Math. Surv. 30 (n° 3) (1975), 55-105. | Zbl | MR

[22] C. Fefferman - The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65. | Zbl | MR | EuDML | DOI

[23] G. B. Folland and J. J. Kohn - The Neumann problem for the Cauchy-Riemann complex, Ann. of Math. Studies 75 (1972), Princ. Univ. Press, Princeton. | Zbl | MR

[24] J. E. Fornaess and N. Sibony - Construction of p.s.h. functions on weakly pseudoconvex domains, Duke Math. J. Vol. 58 n° 3 (1989), 633-655. | Zbl | MR

[25] P. Greiner - On subelliptic estimates for the $\bar{\partial}$ -Neumann problem in $𝐂^{2}$ , J. of Diff. Geom. 9 (1974), 239-250. | Zbl | DOI

[26] P. Greiner and E. Stein - Estimates for the $\bar{\partial}$ -Neumann problem, Math. Notes n° 19, Princ. Univ. Press (1977). | Zbl

[27] K. Hasegawa - Subelliptic estimates for the $\bar{\partial}$ -Neumann problem on certain weakly pseudoconvex domains, J. Fac. Sc. Univ. Tokyo, Sec. IA, vol. 39 n° 3 (1992), 385-418. | Zbl

[28] B. Helffer et J. Nourrigat - Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, Prog. in Math. 58, Birkhaüser, 1985. | Zbl | MR | Numdam

[29] L. H. Ho - Subellipticity of the $\bar{\partial}$ -Neumann problem on non-pseudoconvex domains, Trans. A.M.S. 291 (1985), 43-73. | Zbl

[30] L. Hörmander - An introduction to complex analysis in several variables, Van Nostrand, Princeton, 1966. | Zbl | MR

[31] L. Hormander - $L^{2}$ -estimates and existence theorems for the $\bar{\partial}$ -operator, Acta Math. 113 (1965), 89-152. | Zbl | DOI

[32] L Hörmander - Hypoelliptic second order equations, Acta Math. 119 (1967), 147-171. | Zbl | MR | DOI

[33] L. Hörmander - Subelliptic operators. Seminar on singularities of solutions of linear P.D.E., Ann. of Math. Studies 91 (1978), Princeton. | Zbl | MR

[34] N. Kerzman - The Bergman kernel. Differentiability at the boundary, Math. Ann. 195 (1972), 149-158. | Zbl | MR | EuDML

[35] J. J. Kohn - Harmonic integrals on strongly pseudoconvex manifolds I, Ann. of Math. 78 (1963), 112-148 ; II, Ann. of Math. 79 (1964), 450-472. | Zbl | DOI

[36] J. J. Kohn -Global regularity for $\bar{\partial}$ on weakly pseudoconvex manifolds, Trans. A.M.S. 181 (1973), 273-292. | Zbl

[37] J. J. Kohn -Boundary behavior of $\bar{\partial}$ on weakly pseudoconvex manifolds of dimension two, J. of Diff. Geom. 6 (1972), 523-542. | Zbl | DOI

[38] J. J. Kohn -Subellipticity of the $\bar{\partial}$ -Neumann problem on pseudoconvex domains, Acta Math. 142 (1979), 79-122. | Zbl

[39] J. J. Kohn -Pseudodifferential operators and applications, Proc. Symp. Pure Math. 43, 207-219. | Zbl | MR

[40] J. J. Kohn and L. Nirenberg -Non coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443-492. | Zbl | MR | DOI

[41] J. J. Kohn and L. Nirenberg -A pseudoconvex domain not admitting a holomorphic support function, Math. Ann. 201 (1973), 265-268. | Zbl | MR | EuDML | DOI

[42] N. Lerner -Non solvability in $L^{2}$ for a first order operator satisfying condition $(ψ)$ , Ann. of Math. 139 (1994), 363-393. | Zbl | DOI

[43] H. M. Maire -Hypoelliptic overdetermined systems of partial differential equations, Comm. in P.D.E. 5 (4) (1980), 331-380. | Zbl | MR | DOI

[44] C. B. Morrey -The analytic embedding of abstract real analytic manifolds, Ann. of Math. 68 (1958), 159-201. | Zbl | MR | DOI

[45] L. Nirenberg and F. Trèves -On local solvability for linear partial differential equations I, Comm. Pure Appl. Math. 23 (1970), 1-38. | Zbl | MR | DOI

[46] J. Nourrigat - Reduction microlocale des systèmes d'opérateurs pseudodifférentiels, Ann. Inst. Fourier, Tome XXXVI, Fasc. 3 (1986). | Numdam | Zbl | EuDML | DOI

[47] L. Rothschild and E. Stein - Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1977), 248-315. | Zbl | MR

[48] N. Sibony - Une classe de domaines pseudoconvexes, Duke Math. J. 55 (1987), 299-319. | Zbl | MR | DOI

[49] H. Skoda - Application des techniques $L^{2}$ à la théorie des idéaux de fonctions holomorphes avec poids, Ann. Sc. Ec. Norm. Sup. IV, Série 5 (1972), 545-580. | Numdam | Zbl | MR | EuDML | DOI

[50] D. C. Spencer - Overdetermined systems of linear partial differential equations, Bull. AMS 75 (1969), 179-239. | Zbl | MR | DOI

[51] W. J. Sweeney - A condition for subellipticity in Spencer's Neumann problem, J. of Diff. Geom. 21 (1976), 316-362. | Zbl | MR