Results 101 to 110 of about 139 (131)

Strong hyperbolicity in Gevrey classes

Journal of Differential Equations, 2021
In this paper, the authors consider the Cauchy problem \[ \begin{cases} P(t,\partial_t,\partial_x)u(t,x)=0,\quad(t,x)\in[0,T]\times\mathbb R\\ \partial_t^ju(0,x)=u_j(x),\quad x\in\mathbb R,\quad j=0,...,m-1 \end{cases}\tag{CP} \] where \(P\) is a differential operator of order \(m\) with respect to \(t\) written in the form \[P(t,\partial_t,\partial_x)=
Ferruccio Colombini, Nicola Orrù, Giovanni Taglialatela   +2 more
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FBI transforms in Gevrey classes

Journal d'Analyse Mathématique, 1997
The following theorem is proved: Let \({\mathcal O}\) be a Gevrey \(s\) strictly convex obstacle, \(1 \leq s < 3\). Then for every positive \(\varepsilon\) there are only finitely many resonances in the region \(\{ k \in {\mathbb C} \mid\text{Re }k \geq 1, \text{ Im } k \geq -(C_{0, a} - \varepsilon) (\text{Re } k)^{1/3} \}\).
Lascar, Bernard, Lascar, Richard
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On the L∞ stability of Prandtl expansions in the Gevrey class

Science China Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Qi, Wu, Di, Zhang, Zhifei
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Hypoelliptic convolution equations and Gevrey classes

Functional Analysis and Its Applications, 1971
exaly   +2 more sources

GEVREY-HYPOELLIPTICITY FOR A CLASS OF TOTALLY CHARACTERISTIC OPERATORS

Acta Mathematica Scientia, 2000
The paper presents several new results concerning the Gevrey hypoellipticity of the totally characteristic operators of the form \[ P=t^m D^m_t+ \sum^m_{j=1} P_j(t,x, D_x)t^{m-j} D_t^{m-j}, \] where \(x\in \mathbb{R}^n\) denotes the tangential variable, and \(t\geq 0\) is the normal variable (with the boundary at \(t=0)\).
Tian, Yan, Zhou, Di, Chen, Hua
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Smoothing effect in Gevrey classes for Schrodinger equations

ANNALI DELL UNIVERSITA DI FERRARA, 1999
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Cauchy Problem in the Gevrey Classes

2017
In Chap. 6 we showed that there exists a second order differential operator of spectral type 2 on Σ with bicharacteristics tangent to the double characteristic manifold for which the Cauchy problem is ill-posed in the Gevrey class of order s for any s > 5 even though the Levi condition is satisfied.
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Multi-anisotropic Gevrey classes and ultradistributions

2008
We consider a relevant generalization of the standard Gevrey classes, the so-called multi-anisotropic spaces, defined in terms of a given complete polyhedron. With respect to the previous literature on the subject, we concentrate here in the study of the topology. It is defined as inductive and projective limit of Banach spaces, in two equivalent ways,
Calvo, Daniela, MORANDO, Alessandro
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Gevrey-hypoellipticity and pseudo-differential operators on Gevrey class

1987
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Iterates of a class of hypoelliptic operators and generalized Gevrey classes

1980
Functions of a generalized Gevrey class are characterized by means of $L^2$-estimates of the iterates of a hypoelliptic operator with variable coefficients. The result contains previous ones obtained by T. Kotake and M. S. Narasimhan [Bull. Soc. France 90 (1962), 449--471], E. Newberger and Z. Zielezny [Proc. Amer. Math. Soc.
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