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Medientyp:
E-Artikel
Titel:
Gevrey Hypo-Ellipticity for Sums of Squares of Vector Fields in ℝ 2 with Quasi-Homogeneous Polynomial Vanishing
Beteiligte:
Bove, Antonio;
Tartakoff, David S.
Erschienen:
Department of Mathematics of Indiana University, 2015
Erschienen in:
Indiana University Mathematics Journal, 64 (2015) 2, Seite 613-633
Sprache:
Englisch
ISSN:
0022-2518;
1943-5258
Entstehung:
Anmerkungen:
Beschreibung:
Analytic and Gevrey hypo-ellipticity are studied for operators of the form $P(x,y,D_x,D_y)=D^2_x+\sum_{j=1}^{N}(p_j(x,y)D_y)^2$, in ℝ2. We assume that the vector fields Dx and pj(x,y)Dy satisfy Hörmander's condition, that is, that they as well as their Poisson brackets generate a two-dimensional vector space. It is also assumed that the polynomials pj are quasi-homogeneous of degree mj, that is, that $p_j(\lambda x,\lambda ^\theta y)=\lambda ^{m_j}p_j(x,y)$, for every positive number λ. We prove that if the associated Poisson-Trèves stratification is not symplectic, then P is Gevrey s hypo-elliptic for an s which can be explicitly computed. On the other hand, if the stratification is symplectic, then P is analytic hypo-elliptic.