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. Peloso
Ultimo
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.
eigenvalues of the Levi form; Hormander's Z(q) condition; Cauchy-Riemann equations; Sobolev topology
Settore MAT/05 - Analisi Matematica
2001
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/341213
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