Displaying similar documents to “On the compactness of the ∂ ¯ -Neumann operator”

Geometric conditions which imply compactness of the ∂ ¯ -Neumann operator

Emil Straube (2004)

Annales de l’institut Fourier

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For smooth bounded pseudoconvex domains in ℂ 2 , we provide geometric conditions on the boundary which imply compactness of the ∂ ¯ -Neumann operator. It is noteworthy that the proof of compactness does proceed via verifying the known potential theoretic sufficient conditions.

The ∂ ¯ -Neumann operator on Lipschitz q -pseudoconvex domains

Sayed Saber (2011)

Czechoslovak Mathematical Journal

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On a bounded q -pseudoconvex domain Ω in ℂ n with a Lipschitz boundary, we prove that the ∂ ¯ -Neumann operator N satisfies a subelliptic ( 1 / 2 ) -estimate on Ω and N can be extended as a bounded operator from Sobolev ( - 1 / 2 ) -spaces to Sobolev ( 1 / 2 ) -spaces.

On ∂̅-problems on (pseudo)-convex domains

R. Range (1995)

Banach Center Publications

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In this survey we shall tour the area of multidimensional complex analysis which centers around ∂̅-problems (i.e., the Cauchy-Riemann equations) on pseudoconvex domains. Along the way we shall highlight some of the classical milestones as well as more recent landmarks, and we shall discuss some of the major open problems and conjectures. For the sake of simplicity we will only consider domains in ℂ n ; intriguing phenomena occur already in the simple setting of (Euclidean) convex domains....