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Medientyp:
E-Artikel
Titel:
GEVREY HYPOELLIPTICITY FOR SUMS OF SQUARES WITH A NON-HOMOGENEOUS DEGENERACY
Beteiligte:
BOVE, ANTONIO;
TARTAKOFF, DAVID S.
Erschienen:
AMERICAN MATHEMATICAL SOCIETY, 2014
Erschienen in:Proceedings of the American Mathematical Society
Sprache:
Englisch
DOI:
10.1090/S0002-9939-2014-12247-7
ISSN:
1088-6826;
0002-9939
Entstehung:
Anmerkungen:
Beschreibung:
<p>In this paper we consider sums of squares of vector fields in ℝ
2
satisfying Hörmander's condition and with polynomial, but non-(quasi-)homogeneous, coefficients. We obtain a Gevrey hypoellipticity index which we believe to be sharp. The general operator we consider is
$P = X^{2} + Y^{2} + \sum ^{L}_{j=1} Z^{2}_{j}$
, with X = D
x
, Y = a
0
(x, y)x
q−1
D
y
, Z
j
= a
j
(x, y)x
pj−1
y
kj
D
y
, with a
j
(0, 0) ≠ 0, j = 0, 1,..., L and q > p
j
, {k
j
} arbitrary. The theorem we prove is that P is Gevrey-s hypoelliptic for
$s \geq \frac{1}{1-T}$
,
$T = max_{j} \ \frac{q-p_{j}}{qk_{j}}$
.</p>