This paper is the continuation of [FKP2], where the ∂̄-Neumann problem in the Sobolev topology is formulated and studied on pseudoconvex domains in ℂn. In this paper we study the ∂̄-Neumann problem in the topology of W1 on a domain of the so-called class Z(q). The appropriate noncoercive condition on the corresponding bilinear form Q is proved. Optimal estimates for the ∂̄-Neumann problem are then derived. The result is a new canonical solution for the ∂̄ problem giving best possible estimates and a new Hodge theory for the Cauchy-Riemann complex.

Fontana, L., Krantz, S., Peloso, M. (2001). Estimates for the $\overline\partial$-Neumann problem in the Sobolev topology on $Z(q)$ domains. HOUSTON JOURNAL OF MATHEMATICS, 27(1), 123-175.

Estimates for the $\overline\partial$-Neumann problem in the Sobolev topology on $Z(q)$ domains

FONTANA, LUIGI;
2001

Abstract

This paper is the continuation of [FKP2], where the ∂̄-Neumann problem in the Sobolev topology is formulated and studied on pseudoconvex domains in ℂn. In this paper we study the ∂̄-Neumann problem in the topology of W1 on a domain of the so-called class Z(q). The appropriate noncoercive condition on the corresponding bilinear form Q is proved. Optimal estimates for the ∂̄-Neumann problem are then derived. The result is a new canonical solution for the ∂̄ problem giving best possible estimates and a new Hodge theory for the Cauchy-Riemann complex.
Articolo in rivista - Articolo scientifico
Neumann problem
English
2001
27
1
123
175
none
Fontana, L., Krantz, S., Peloso, M. (2001). Estimates for the $\overline\partial$-Neumann problem in the Sobolev topology on $Z(q)$ domains. HOUSTON JOURNAL OF MATHEMATICS, 27(1), 123-175.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/17819
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