Complex vector fields and hypoelliptic partial differential operators

Details Complex vector fields and hypoelliptic partial differential operators Complex vector fields and hypoelliptic partial differential operators

2008-07-30

arxiv.org/abs/0807.4857v2

Ann. Inst. Fourier (Grenoble) 60 (2010), no. 3, 987-1034

Mathematics

Analysis of PDEs

39 pages

Scientific paper

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for $CR$ manifolds and H\"ormander's bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which the distribution of $(0,1)$ vector fields satisfies a subelliptic estimate. v2: minor revision, to appear in Ann. Inst. Fourier

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