Results 121 to 130 of about 4,782 (151)

Global hypoellipticity for a class of overdetermined systems of pseudo-differential operators on the torus

Annali di Matematica Pura ed Applicata, 2020
This article studies the global hypoellipticity of a class of overdetermined systems of pseudo-differential operators defined on the torus. The main goal consists in establishing connections between the global hypoellipticity of the system and the global
Fernando de Ávila Silva, Cleber de Medeira   +1 more
semanticscholar   +1 more source

Global Hypoellipticity and Solvability with Loss of Derivatives on the Torus

Journal of Functional Analysis
This paper provides a complete characterization of global hypoellipticity and solvability with loss of derivatives for Fourier multiplier operators on the $n$-dimensional torus.
A. Kowacs, A. Kirilov
semanticscholar   +1 more source

Global Hypoellipticity for Involutive Systems on Non-Compact Manifolds

Journal of Geometric Analysis
We study the global hypoellipticity of the operator L=dt+∑k=1mωk∧∂xk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
S. Coriasco, A. Kirilov, W. A. D. de Moraes, P. M. Tokoro   +3 more
semanticscholar   +1 more source

Global Hypoellipticity for a Class of Pseudo-differential Operators on the Torus

Journal of Fourier Analysis and Applications, 2018
We show that an obstruction of number-theoretical nature appears as a necessary condition for the global hypoellipticity of the pseudo-differential operator $$L=D_t+(a+ib)(t)P(D_x)$$L=Dt+(a+ib)(t)P(Dx) on $$\mathbb {T}^1_t\times \mathbb {T}_x^{N}$$Tt1 ...
Fernando de Ávila Silva, Rafael B. Gonzalez, A. Kirilov, Cleber de Medeira   +3 more
semanticscholar   +2 more sources

The Hypoelliptic Dirac Operator

2008
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openaire   +2 more sources

Global hypoellipticity for first-order operators on closed smooth manifolds

Journal d'Analyse Mathematique, 2015
The main goal of this paper is to address global hypoellipticity issues for the class of first-order pseudo-differential operators L = Dt + C(t, x,Dx), where (t, x) ∈ T × M, T is the one-dimensional torus, M is a closed manifold, and C(t, x,Dx) is a ...
Fernando de Ávila Silva, T. Gramchev, A. Kirilov   +2 more
semanticscholar   +1 more source

Global analytic hypoellipticity of involutive systems on compact manifolds

Mathematische Annalen, 2022
G. Araújo, P. L. Dattori da Silva, B. D. Lessa Victor   +2 more
semanticscholar   +1 more source

Gevrey Hypoellipticity for Maximally Hypoelliptic Fourth Order Partial Differential Operators

Communications in Partial Differential Equations, 1995
Local C∞ and (sharp) Gevrey hypoellipticity are proved for maximally hypoelliptic fourth order partial differential operators of the form P = D|c|
Petar Radoev Popivanov, David S. Tartakoff   +1 more
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ON A CRITERION FOR HYPOELLIPTICITY

Mathematics of the USSR-Sbornik, 1971
In this paper a criterion for hypoellipticity is proved which is formulated in terms of certain estimates in the norms, and which is a generalization of a criterion of Treves. With the use of this criterion it is possible to prove the hypoellipticity of certain operators that do not satisfy Hormander's criterion.
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Gevrey Hypoellipticity of p-Powers of Non-Hypoelliptic Operators

2004
We characterize the hypoellipticity inC ∞ and GevreyG λ classes of 2-variable PDO’s containing powers of anisotropic principal terms. We use an approach based on methods from microlocal analysis. Conditions are imposed on the coefficients of lower order terms. Also a semilinear version is proposed consideringC ∞ nonlinear perturbations. See Theorem 1.1
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