scholarly journals Propagation of singularities and local solvability in Gevrey classes

1986 ◽  
pp. 1-11
Author(s):  
Luigi Rodino
Keyword(s):  
Local Solvability ◽  
Gevrey Classes ◽  
Propagation Of Singularities

scholarly journals Beyond gevrey regularity: Superposition and propagation of singularities

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2763-2782 ◽  
Author(s):  
Stevan Pilipovic ◽  
Nenad Teofanov ◽  
Filip Tomic
Keyword(s):  
Wave Front ◽  
Regularity Condition ◽  
Differential Operators ◽  
Ultradifferentiable Functions ◽  
Gevrey Regularity ◽  
Gevrey Classes ◽  
Partial Differential Operators ◽  
Wave Front Sets ◽  
Propagation Of Singularities ◽  
Two Parameters

We propose the relaxation of Gevrey regularity condition by using sequences which depend on two parameters, and define spaces of ultradifferentiable functions which contain Gevrey classes. It is shown that such a space is closed under superposition, and therefore inverse closed as well. Furthermore, we study partial differential operators whose coefficients are less regular then Gevrey-type ultradifferentiable functions. To that aim we introduce appropriate wave front sets and prove a theorem on propagation of singularities. This extends related known results in the sense that assumptions on the regularity of the coefficients are weakened.

Hypoellipticity and Local Solvability in Gevrey Classes

2002 ◽  
Vol 242 (1) ◽  
pp. 5-16 ◽  
Author(s):  
Angela A. Albanese ◽  
Andrea Corli ◽  
Luigi Rodino
Keyword(s):  
Local Solvability ◽  
Gevrey Classes

On the local solvability of vector fields with critical points

2011 ◽  
Vol 10 (3) ◽  
pp. 785-808
Author(s):  
François Treves
Keyword(s):  
Critical Points ◽  
Vector Fields ◽  
Local Solvability ◽  
Complex Vector ◽  
Base Manifold ◽  
Smooth Complex ◽  
Empty Subset

AbstractThe article discusses the local solvability (or lack thereof) of various classes of smooth, complex vector fields that vanish on some non-empty subset of the base manifold.

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