Global boundary regularity for the $\overline{\partial}$-equation on $q$-pseudo-convex domains

Ahn, Heungju

Global boundary regularity for the

\bar{p a r t i a l}

-equation on

q

-pseudo-convex domains

Ahn, Heungju

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 16 (2005), p. 5-9 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

For a bounded domain $D$ of $C^{n}$ , we introduce a notion of « $q$ -pseudoconvexity» of new type and prove that for a given $\bar{\partial}$ -closed $(p, r)$ -form $f$ that is smooth up to the boundary on $D$ , and for $r \geq q$ , there exists a $(p, r - 1)$ -form $u$ smooth up to the boundary on $D$ which is a solution of the equation $\bar{\partial} u = f$

Si introduce una nuova nozione di « $q$ -pseudoconvessità» per un dominio $D$ di $C^{n}$ . Per un tale $D$ , e per ogni forma $\bar{\partial}$ -chiusa $f$ di tipo $(p, r)$ con $r \geq q$ , che è $C^{\infty}$ fino al bordo di $D$ , si prova che esiste una forma $u$ anch'essa $C^{\infty}$ in $\bar{D}$ che risolve l'equazione $\bar{\partial} u = f$

Publié le : 2005-03-01

MR 2225919 | Zbl 1225.35157

@article{RLIN_2005_9_16_1_5_0,
     author = {Heungju Ahn},
     title = {Global boundary regularity for the $\overline{\partial}$-equation on $q$-pseudo-convex domains},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {16},
     year = {2005},
     pages = {5-9},
     zbl = {1225.35157},
     mrnumber = {2225919},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2005_9_16_1_5_0}
}

Ahn, 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, Tome 16 (2005) pp. 5-9. http://gdmltest.u-ga.fr/item/RLIN_2005_9_16_1_5_0/

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