1,720,965 research outputs found
(SEMI-)GLOBAL ANALYTIC HYPOELLIPTICITY FOR A CLASS OF "SUMS OF SQUARES" WHICH FAIL TO BE LOCALLY ANALYTIC HYPOELLIPTIC
Full text linkThe global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced by P. Albano, A. Bove, and M. Mughetti, satisfying the Ho spacing diaeresis rmander condition and which fail to be either locally or microlocally analytic hypoelliptic
On the sharp Gevrey regularity for a generalization of the M\'etivier operator
Full text linkThe sharp Gevrey hypoellipticity is provided for the following generalization
of the M\'etivier operator, "Non-hypoellipticit\'e analytique pour
" by G. M\'etivier,
\begin{align*}
D_{x}^{2}+\left(x^{2n+1}D_{y}\right)^{2}+\left(x^{n}y^{m}D_{y}\right)^{2},
\end{align*} in open neighborhood of the origin in ,
where and are positive integers
A proof of hypoellipticity for Kohn’s operator via FBI
No full textA new proof of both analytic and C∞ hypoellipticity of Kohn's operator is given using FBI techniques introduced by J. Sjöstrand. The same proof allows us to obtain both kind of hypoellipticity at the same time
On the partial and microlocal regularity for generalized Métivier operators
Full text linkThe partial and the microlocal regularity are provided via L2-estimate and via FBI transform respectively, for the following generalization of the Métivier operato
Germ hypoellipticity and loss of derivatives
No full textWe prove hypoellipticity in the sense of germs for the operator
where
even though it fails to be hypoelliptic in the strong sense. The primary tool is an a priori estimate.</p
On a sum of squares operator related to the Schrödinger equation with a magnetic field
No full textWe study the analytic and Gevrey regularity for a “sum of squares” operator closely connected to the Schrödinger equation with minimal coupling. We however assume that the (magnetic) vector potential has some degree of homogeneity and that the Hörmander bracket condition is satisfied. It is shown that the local analytic/Gevrey regularity of the solution is related to the multiplicities of the zeroes of the Lie bracket of the vector fields
On the microlocal regularity of the analytic vectors for "sums of squares" of vector fields
Full text linkWe prove via FBI-transform a result concerning the microlocal Gevrey regularity of analytic vectors for operators sums of squares of vector fields with real-valued real analytic coefficients of Hormander type, thus providing a microlocal version, in the analytic category, of a result due to Derridj (Pac J Math 302(2):511-543, 2019) concerning the problem of the local regularity for the Gevrey vectors for sums of squares of vector fields with real-valued real analytic/Gevrey coefficients
On a class of globally analytic hypoelliptic operators with non-negative characteristic form
No full textThe global analytic hypoellipticity is proved for a class of second order partial differential equations with non-negative characteristic form globally defined on the torus. The class considered in this work generalizes at some degree the class of sum of squares considered by Bove-Chinni and also by Cordaro-Himonas
LOWER ORDER PERTURBATION AND GLOBAL ANALYTIC VECTORS FOR A CLASS OF GLOBALLY ANALYTIC HYPOELLIPTIC OPERATORS
No full textIn this work we return to the class of globally analytic hypoelliptic Hormander's operators defined on the N-dimensional torus introduced by Cordaro and Himonas and prove that if P is any operator in this class, then a perturbation of P by an analytic pseudodifferential operator with degree smaller than the subelliptic index of P remains globally analytic hypoelliptic. We also study the Gevrey regularity of the Gevrey vectors for such a class and at the end we also show that Cordaro and Himonas's result can be extended to a similar class of operators now defined in a product of compact Lie group by a compact manifold
On a class of sums of squares related to Hamiltonians with a non periodic magnetic field
Full text linkWe consider the operator in (1.1) and prove that it is analytic hypoelliptic. This operator is linked to a stationary Schrödinger equation with a magnetic field and an anharmonic type potential. It is also a sum of squares of vector fields exhibiting a symplectic characteristic variety. This aspect is discussed in the introduction
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