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On the Hypoellipticity of Differential Forms with Isolated Singularities

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Abstract

Hypoellipticity for a class of germs of ℂ-valued, real-analytic 1-forms with an isolated singularity is studied. The main result states that in dimension ≥3 such forms are real-analytic hypoelliptic over L p functions, but are not real-analytic hypoelliptic in dimension 2. The case of C ∞-hypoellipticity for a class of rotation invariant forms in ℝ2 is also considered.

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Authors and Affiliations

  1. Department of Mathematics, Florida International University, Miami, FL, 33199, USA

    Abdelhamid Meziani

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  1. Abdelhamid Meziani
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Correspondence to Abdelhamid Meziani.

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Communicated by Steven R. Bell.

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Meziani, A. On the Hypoellipticity of Differential Forms with Isolated Singularities. J Geom Anal 23, 1236–1256 (2013). https://doi.org/10.1007/s12220-011-9285-x

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  • DOI: https://doi.org/10.1007/s12220-011-9285-x

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