| Title:
|
The $\overline\partial $-Neumann operator on strongly pseudoconvex domain with piecewise smooth boundary (English) |
| Author:
|
Abdelkader, Osama |
| Author:
|
Saber, Sayed |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
317-328 |
| . |
| Category:
|
math |
| . |
| MSC:
|
32W05 |
| MSC:
|
35F15 |
| idZBL:
|
Zbl 1108.35027 |
| idMR:
|
MR2181009 |
| . |
| Date available:
|
2009-09-25T14:26:32Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/131025 |
| . |
| Reference:
|
[1] BOAS H. P.-STRAUBE E. J.: Equivalence of regularity for the Bergman projection and the $\overline\partial$-Neumann operator.Manuscripta Math. 67 (1990), 25-33. MR 1037994 |
| Reference:
|
[2] BOAS H. P.-STRAUBE E. J.: Sobolev estimates for the $\overline\partial$-Neumann operator on domains in Cn admitting a defining function that is plurisubharmonic on the boundary.Math. Z. 206 (1991), 81-88. MR 1086815 |
| Reference:
|
[3] BOAS H. P.-STRAUBE E. J.: Global regularity of the $\overline\partial$-Neumann problem: A Survey of the $L^2$-Sobolev theory.In: Several Complex Variables (M. Schneider et al., eds.), Math. Sci. Res. Inst. Publ. 37, Cambridge University Press, Cambridge, 1999, pp. 79-111. MR 1748601 |
| Reference:
|
[4] BONAMI A.-CHARPENTIER P.: Boundary values for the canonical solution to $\overline\partial$-equation and $W^{1/2$ -estimates.Preprint, Bordeaux, 1990. MR 1055987 |
| Reference:
|
[5] CHEN S.-C-SHAW M.-C: Partial Differential Equations in Several Complex Variables.Stud. Adv. Math. 19, AMS-International Press, Providence, RI, 2001. MR 1800297 |
| Reference:
|
[6] EHSANI D.: Analysis of the $\overline\partial$-Neumann problem along a straight edge.Preprint Math. CV/0309169. Zbl 1057.32015, MR 2091680 |
| Reference:
|
[7] EHSANI D.: Solution of the d-bar-Neumann problem on a bi-disc.Math. Res. Lett. 10 (2003), 523-533. MR 1995791 |
| Reference:
|
[8] EHSANI D.: Solution of the d-bar-Neumann problem on a non-smooth domain.Indiana Univ. Math. J. 52 (2003), 629-666. MR 1986891 |
| Reference:
|
[9] ENGLIŠ M.: Pseudolocal estimates for $\overline\partial$ on general pseudoconvex domains.Indiana Univ. Math. J. 50 (2001), 1593-1607. Zbl 1044.32029, MR 1889072 |
| Reference:
|
[10] FOLLAND G. B.-KOHN J. J.: The Neumann Problem for the Cauchy-Riemann Complex.Princeton University Press, Princeton, 1972. Zbl 0247.35093, MR 0461588 |
| Reference:
|
[11] GRISVARD P.: Elliptic Problems in Nonsmooth Domains.Monogr. and Stud, in Math. 24. Pitman Advanced Publishing Program, Pitman Publishing Inc., Boston-London-Melbourne, 1985. Zbl 0695.35060, MR 0775683 |
| Reference:
|
[12] HENKIN G.-IORDAN A.-KOHN J. J.: Estimations sous-elliptiques pour le problem $\overline\partial$-Neumann dans un domaine strictement pseudoconvexe a frontiere lisse par morceaux.C. R. Acad. Sci. Paris Ser. I Math. 323 (1996), 17-22. MR 1401622 |
| Reference:
|
[13] HÖRMANDER L.: $L^2$ -estimates and existence theorems for the $\overline\partial$-operator.Acta Math. 113 (1965), 89-152. Zbl 0158.11002, MR 0179443 |
| Reference:
|
[14] KOHN J. J.: Harmonic integrals on strongly pseudo-convex manifolds I.Ann. Math. (2) 78 (1963), 112-148. Zbl 0161.09302, MR 0153030 |
| Reference:
|
[15] KOHN J. J.: Global regularity for $\overline\partial$ on weakly pseudoconvex manifolds.Trans. Amer. Math. Soc 181 (1973), 273-292. MR 0344703 |
| Reference:
|
[16] KOHN J. J.: Subellipticity of the $\overline\partial$-Neumann problem on pseudoconvex domains: Sufficient conditions.Acta Math. 142 (1979), 79-122. MR 0512213 |
| Reference:
|
[17] KOHN J. J.: A survey of the $\overline\partial$ -Neumann problem.In: Complex Analysis of Several Variables (Yum-Tong Siu, ed.), Proc Sympos. Pure Math. 41, Amer. Math. Soc, Providence, RI, 1984, pp. 137-145. MR 0740877 |
| Reference:
|
[18] KRANTZ S. G.: Partial Differential Equations and Complex Analysis.CRC Press, Boca Raton, 1992. Zbl 0852.35001, MR 1207812 |
| Reference:
|
[19] MICHEL J.-SHAW M.-C.: Subelliptic estimates for the $\overline\partial$-Neumann operator on piecewise smooth strictly pseudoconvex domains.Duke Math. J. 93 (1998), 115-128. Zbl 0953.32027, MR 1620087 |
| Reference:
|
[20] MICHEL J.-SHAW M.-C: The $\overline\partial$-Neumann operator on Lipschitz pseudoconvex domains with plurisubharmonic defining functions.Duke Math. J. 108 (2001), 421-447. Zbl 1020.32030, MR 1838658 |
| Reference:
|
[21] SHAW M.-C.: Local existence theorems with estimates for $\overline\partial_b$ on weakly pseudo-convex $CR$ manifolds.Math. Ann. 294 (1992), 677-700. MR 1190451 |
| Reference:
|
[22] STEIN E. M.: Singular Integrals and Differentiability Properties of Functions.Princeton Math. Ser. 30, Princeton Univ. Press, Princeton, NJ, 1970. Zbl 0207.13501, MR 0290095 |
| Reference:
|
[23] STRAUBE E. : Plurisubharmonic functions and subellipticity of the $\overline\partial$-Neumann problem on nonsmooth domains.Math. Res. Lett. 4 (1997), 459-467. MR 1470417 |
| . |
