On the Hypoellipticity of Differential Forms with Isolated Singularities

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 ∞ -hypoellip...

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Veröffentlicht in:	The Journal of Geometric Analysis 2013-07, Vol.23 (3), p.1236-1256
1. Verfasser:	Meziani, Abdelhamid
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics
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Zusammenfassung:	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 ℝ 2 is also considered.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-011-9285-x