Geometric conditions which imply compactness of the ${\overline{\partial }}$-Neumann operator

Straube, Emil

Geometric conditions which imply compactness of the

\bar{\partial}

-Neumann operator
[Conditions géométriques qui entraînent la compacité de l’opérateur

\bar{\partial}

-Neumann]

Straube, Emil

Annales de l'Institut Fourier, Tome 54 (2004), p. 699-710 / Harvested from Numdam

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Résumé
Abstract

On donne, pour les domaines lisses bornés pseudoconvexes de $ℂ^{2}$ , des conditions géométriques concernant le bord qui entraînent la compacité de l’opérateur $\bar{\partial}$ -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 $\bar{\partial}$ -Neumann operator. It is noteworthy that the proof of compactness does not proceed via verifying the known potential theoretic sufficient conditions.

Publié le : 2004-01-01

MR 2097419 | Zbl 1061.32028

DOI : https://doi.org/10.5802/aif.2030
Classification: 32W05
Mots clés: opérateur

\bar{\partial}

-Neumann, compacité, conditions géométriques

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     title = {Geometric conditions which imply compactness of the ${\overline{\partial }}$-Neumann operator},
     journal = {Annales de l'Institut Fourier},
     volume = {54},
     year = {2004},
     pages = {699-710},
     doi = {10.5802/aif.2030},
     mrnumber = {2097419},
     zbl = {1061.32028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2004__54_3_699_0}
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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) pp. 699-710. doi : 10.5802/aif.2030. http://gdmltest.u-ga.fr/item/AIF_2004__54_3_699_0/

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