Global boundary regularity for the -equation on -pseudo-convex domains
- Volume: 16, Issue: 1, page 5-9
- ISSN: 1120-6330
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topAhn, Heungju. "Global boundary regularity for the $\overline{\partial}$-equation on $q$-pseudo-convex domains." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 16.1 (2005): 5-9. <http://eudml.org/doc/252429>.
@article{Ahn2005,
abstract = {For a bounded domain $D$ of $\mathbb\{C\}^\{n\}$, we introduce a notion of «$q$-pseudoconvexity» of new type and prove that for a given $\overline\{\partial\}$-closed $(p,r)$-form $f$ that is smooth up to the boundary on $D$, and for $r \ge q$, there exists a $(p,r-1)$-form $u$ smooth up to the boundary on $D$ which is a solution of the equation $\overline\{\partial\} u = f$},
author = {Ahn, Heungju},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {$\overline\{\partial \}$
∂
¯
-equation; $q$
q
-pseudoconvexity; Cauchy-Riemann system; -equation; -pseudoconvexity},
language = {eng},
month = {3},
number = {1},
pages = {5-9},
publisher = {Accademia Nazionale dei Lincei},
title = {Global boundary regularity for the $\overline\{\partial\}$-equation on $q$-pseudo-convex domains},
url = {http://eudml.org/doc/252429},
volume = {16},
year = {2005},
}
TY - JOUR
AU - Ahn, Heungju
TI - Global boundary regularity for the $\overline{\partial}$-equation on $q$-pseudo-convex domains
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2005/3//
PB - Accademia Nazionale dei Lincei
VL - 16
IS - 1
SP - 5
EP - 9
AB - For a bounded domain $D$ of $\mathbb{C}^{n}$, we introduce a notion of «$q$-pseudoconvexity» of new type and prove that for a given $\overline{\partial}$-closed $(p,r)$-form $f$ that is smooth up to the boundary on $D$, and for $r \ge q$, there exists a $(p,r-1)$-form $u$ smooth up to the boundary on $D$ which is a solution of the equation $\overline{\partial} u = f$
LA - eng
KW - $\overline{\partial }$
∂
¯
-equation; $q$
q
-pseudoconvexity; Cauchy-Riemann system; -equation; -pseudoconvexity
UR - http://eudml.org/doc/252429
ER -
References
top- CHEN, S.-C. - SHAW, M.-C., Partial differential equations in several complex variables. AMS/IP Studies in Advanced Mathematics, vol. 19, American Mathematical Society, Providence, RI2001. MR 2001m:32071 Zbl0963.32001MR1800297
- HO, L.-H., -problem on weakly -convex domains. Math. Ann., 290, no. 1, 1991, 3-18. MR 92j:32052 Zbl0714.32006MR1107660DOI10.1007/BF01459235
- KOHN, J.J., Global regularity for on weakly pseudo-convex manifolds. Trans. Amer. Math. Soc., 181, 1973, 273-292. MR 49 #9442 Zbl0276.35071MR344703
- KOHN, J.J., Methods of partial differential equations in complex analysis. Amer. Math. Soc. Proc. Sympos. Pure Math., XXX, Part. 1, Providence, RI1977, 215-237. Zbl0635.32011MR477156
- MICHEL, V., Sur la régularité du au bord d'un domaine de dont la forme de Levi a exactement valeurs propres strictement négatives. Math. Ann., 295, 1993, no. 1, 135-161. MR 93k:32030 Zbl0788.32010MR1198845DOI10.1007/BF01444880
- ZAMPIERI, G., -pseudoconvexity and regularity at the boundary for solutions of the -problem. Compositio Math., 121, 2000, no. 2, 155-162. MR 2001a:32048 Zbl0953.32030MR1757879DOI10.1023/A:1001811318865
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