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Precise subelliptic estimates for a class of special domains

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Abstract

For the \(\bar \partial \)-Neumann problem on a regular coordinate domain Ω ⊂ ℂn+1, we prove ∈-subelliptic estimates for an index ∈ ≥ (2m)−1, where m is the “multiplicity”. We also intend to supply here a much simplified proof of the existing literature. Our approach is founded on the method by Catlin in [2], which consists of constructing a bounded family of weights {φδ} whose Levi form is bigger than δ-2∊ on the δ -strip around ∂Ω.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Blk S17, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore

    Tran Vu Khanh

  2. Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121, Padova, Italy

    Giuseppe Zampieri

Authors
  1. Tran Vu Khanh
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  2. Giuseppe Zampieri
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Correspondence to Tran Vu Khanh.

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Khanh, T.V., Zampieri, G. Precise subelliptic estimates for a class of special domains. JAMA 123, 171–181 (2014). https://doi.org/10.1007/s11854-014-0017-6

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  • DOI: https://doi.org/10.1007/s11854-014-0017-6

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