For smooth bounded pseudoconvex domains in , 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.
On donne, pour les domaines lisses bornés pseudoconvexes de , 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.
Keywords: $\overline{\partial }$-Neumann operator, compactness, geometric conditions
Mot clés : opérateur $\overline{\partial }$-Neumann, compacité, conditions géométriques
Straube, Emil 1
@article{AIF_2004__54_3_699_0, author = {Straube, Emil}, title = {Geometric conditions which imply compactness of the ${\overline{\partial }}${-Neumann} operator}, journal = {Annales de l'Institut Fourier}, pages = {699--710}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {3}, year = {2004}, doi = {10.5802/aif.2030}, zbl = {1061.32028}, mrnumber = {2097419}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2030/} }
TY - JOUR AU - Straube, Emil TI - Geometric conditions which imply compactness of the ${\overline{\partial }}$-Neumann operator JO - Annales de l'Institut Fourier PY - 2004 SP - 699 EP - 710 VL - 54 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2030/ DO - 10.5802/aif.2030 LA - en ID - AIF_2004__54_3_699_0 ER -
%0 Journal Article %A Straube, Emil %T Geometric conditions which imply compactness of the ${\overline{\partial }}$-Neumann operator %J Annales de l'Institut Fourier %D 2004 %P 699-710 %V 54 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2030/ %R 10.5802/aif.2030 %G en %F AIF_2004__54_3_699_0
Straube, Emil. Geometric conditions which imply compactness of the ${\overline{\partial }}$-Neumann operator. Annales de l'Institut Fourier, Volume 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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