no. 3
Geometric conditions which imply compactness of the ∂ ¯-Neumann operator
[Conditions géométriques qui entraînent la compacité de l’opérateur ∂ ¯-Neumann]
Straube, Emil1
1 Department of Mathematics, Texas A\&M University, College Station, TX 77843, (USA)
Annales de l'Institut Fourier, Tome 54 (2004) no. 3, pp. 699-710.

On donne, pour les domaines lisses bornés pseudoconvexes de ℂ 2 , des conditions géométriques concernant le bord qui entraînent la compacité de l’opérateur ∂ ¯-Neumann. Il est remarquable que la preuve de la compacité ne procède pas par verification des conditions suffisantes bien connues de type théorie du potentiel.

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 not proceed via verifying the known potential theoretic sufficient conditions.

DOI : 10.5802/aif.2030
Classification : 32W05
Keywords: $\overline{\partial }$-Neumann operator, compactness, geometric conditions
Mot clés : opérateur $\overline{\partial }$-Neumann, compacité, conditions géométriques

Straube, Emil 1

1 Department of Mathematics, Texas A\&M University, College Station, TX 77843, (USA) 
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Straube, Emil. Geometric conditions which imply compactness of the ${\overline{\partial }}$-Neumann operator. Annales de l'Institut Fourier, Tome 54 (2004) no. 3, pp. 699-710. doi : 10.5802/aif.2030. https://aif.centre-mersenne.org/articles/10.5802/aif.2030/

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