Results 131 to 140 of about 1,300,131 (168)

Gevrey hypoellipticity of a class of pseudodifferential operators

Gevrey hypoellipticity of a class of pseudodifferential operators
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On Some Generalizations of Gevrey Classes

Mathematische Nachrichten, 2011
We present a generalization of Gevrey classes, aiming at including the inhomogeneous Gevrey functions introduced by Liess 15 and the ultradifferentiable functions in the sense of Braun et al. 4. Therefore, we treat the related dual spaces, called generalized Gevrey ultradistributions, proving also a version of the Paley-Wiener-Schwartz Theorem in our ...
Daniela Calvo, María del Carmen Gómez-Collado   +1 more
exaly   +5 more sources

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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Hypoellipticity and Local Solvability in Gevrey Classes

Mathematische Nachrichten, 2002
As standard, let \(G^s ...
Angela A Albanese, Luigi Rodino
exaly   +5 more sources

NONLINEAR HYPERBOLIC CAUCHY PROBLEMS IN GEVREY CLASSES

Chinese Annals of Mathematics, 2001
The authors consider the quasilinear Cauchy problem \[ \sum_{ |\alpha|\leq m}a_\alpha (t,x,D^\beta_{t,x} u)D^\alpha_{t,x} u=f(t,x, D^\beta_{t,x}u), \] \[ D^j_t u|_{t=0}=0,\;0\leq ...
CICOGNANI M., ZANGHIRATI, Luisa
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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
exaly   +3 more sources

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
core   +3 more sources

Global Hypoellipticity and Global Solvability in Gevrey Classes on the n-Dimensional Torus

Journal of Differential Equations, 2004
Let P be a linear partial differential operator with coefficients in the Gevrey class Gs(Tn) where Tn is the n-dimensional torus and s⩾1. We prove that if P is s-globally hypoelliptic in Tn then its transposed operator tP is s-globally solvable in Tn ...
ALBANESE, Angela Anna, ZANGHIRATI L., Albanese A. A.   +2 more
exaly   +2 more sources

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
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Chen, Qi, Wu, Di, Zhang, Zhifei
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