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The \(\bar{\partial }\)-Neumann problem on the intersection of two weakly q-convex domains

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We establish some functional analytic properties for the \(\bar{\partial }\)-Neumann operator \(N_s\) on the intersection of two bounded weakly q-convex domains with \(\mathcal {C}^2\)-boundaries in \(\mathbb {C}^n\). Attention is focussed on questions of \(L^2\)-existence and compactness of \(N_s\) for all \(s\ge q\). Sobolev and boundary regularity for the \(\bar{\partial }\)-equation are consequently achieved.

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, University of Jeddah, 21589, Jeddah, Saudi Arabia

    Shaban Khidr

  2. Mathematics Department and computer sciences, Faculty of Science, Beni-Suef University, 62511, Beni-Suef, Egypt

    Shaban Khidr

  3. Mathematics Department, UFR of Science and Technology, Assane Seck University of Ziguinchor, 27000, Ziguinchor, Sénégal

    Salomon Sambou

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  1. Shaban Khidr
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  2. Salomon Sambou
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Correspondence to Shaban Khidr.

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Khidr, S., Sambou, S. The \(\bar{\partial }\)-Neumann problem on the intersection of two weakly q-convex domains. Ricerche mat 72, 739–752 (2023). https://doi.org/10.1007/s11587-021-00576-2

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  • DOI: https://doi.org/10.1007/s11587-021-00576-2

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