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.
Estimates for the (delta)over-bar-Neumann problem in the Sobolev topology on Z(q) domains / L. Fontana, S.G. Krantz, M.M. Peloso. - In: HOUSTON JOURNAL OF MATHEMATICS. - ISSN 0362-1588. - 27:1(2001), pp. 123-175.
Estimates for the (delta)over-bar-Neumann problem in the Sobolev topology on Z(q) domains
M.M. PelosoUltimo
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.Pubblicazioni consigliate
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