Propagation of Singularities and Semi-Global Existence Theorems for (Pseudo)-Differential Operators of Principal Type

1978 ◽  
Vol 108 (3) ◽  
pp. 569 ◽  
Author(s):  
Lars Hormander
Keyword(s):  
Global Existence ◽  
Differential Operators ◽  
Existence Theorems ◽  
Principal Type ◽  
Pseudo Differential Operators ◽  
Propagation Of Singularities

scholarly journals Propagation of singularities for non-real pseudo-differential operators

1994 ◽  
Vol 64 (1) ◽  
pp. 263-289 ◽  
Author(s):  
Bernard Lascar ◽  
Richard Lascar ◽  
Nicolas Lerner
Keyword(s):  
Differential Operators ◽  
Pseudo Differential Operators ◽  
Propagation Of Singularities

Some results on hypoelliptic pseudo-differential operators

1970 ◽  
Vol 68 (3) ◽  
pp. 685-695
Author(s):  
Robert J. Elliott
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Normal Operator ◽  
A Priori ◽  
Adjoint Operator ◽  
Elliptic Operators ◽  
Pseudo Differential Operator ◽  
Principal Type ◽  
Subelliptic Operators ◽  
Pseudo Differential Operators

In this paper, by extending the results of Yoshikawa (8), we obtain local a priori inequalities for hypoelliptic pseudo-differential operators. Using these inequalities we then show how the results of Hormander ((3), Theorem 8·7·2), on the solvability of the adjoint operator of a principally normal operator can be extended to the adjoint operator of a hypoelliptic pseudo-differential operator. Finally, we consider a class of operators which satisfy more particular a priori inequalities and we show that these operators are hypoelliptic. This class of operators was studied by Egorov (1), and he shows them to be ‘of principal type’. They include elliptic operators and also the subelliptic operators of Hormander (4).

Propagation Of Singularities for Semilinear Hyperbolic Equations

1993 ◽  
Vol 45 (4) ◽  
pp. 835-846
Author(s):  
Linqi Liu
Keyword(s):  
Sobolev Space ◽  
Differential Operators ◽  
Weighted Sobolev Space ◽  
Hyperbolic Equations ◽  
Second Order ◽  
Pseudo Differential Operators ◽  
Propagation Of Singularities

AbstractIn this paper we use a particular kind of weighted Sobolev space and pseudo-differential operators to study H3s propagation of singularities for the solution u ∊ Hs of the equations with second order.

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