Analyticité globale de la solution du problème ∂¯-Neumann pour une classe de domaines de ℂn

✍ Scribed by Isabelle Reizner

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 381 KB
• Volume: 324
• Category: Article
• ISSN: 0764-4442
• DOI: 10.1016/s0764-4442(99)80405-4

✦ Synopsis

R&urn&

Soit al un domaine born& rkgulier et pseudoconvexe de C", dCfini par 0 = {]wI' + p(z> 2) < (I}, oh /, est plurisousharmonique et analytique rkelle sur CS-'. Alors, si on suppose de plus que p est stritement plurisousharmonique sur {p 5 I)}, on obtient la rCgularit& analytique rCelle globale du problkme de Neumann pour i, sur $1 pour les (O,q)-formes.

-Global analyticity

for the &Neumann problem on some domains of C" Abstract.

Let 12 be a bounded, regular und pseudoconvex domain in C", 61 = { ~IU/~ + p(z. 2) < 0}, where p is plurisubharmonic and real analytic on Cl.'-'. Then, if we suppose thut p is strictly plurisubharmonic on {p = 0}, we have the global real unalytic regu1arit.y of the &Neumann problem on 62 for the (0, q)7form,s,

Abridged Engiish Version

Consider the &Neumann problem on 12:

where f is a (O! q)-form (1 5 q 5 II. -1). In this Note, we show the following theorem:

THEOREM.

-Let I2 be a bounded domain of C", such that:

(**I