Regularity and Solvability of Pseudo-differential Operators with Double Characteristics

This paper deals with several classes of pseudo-differential operators with double involutive characteristics as well as operators with double involutive–symplectic characteristics. In the first case, microlocal non-solvability is shown, while in the second case, the conditions imposed on the subpri...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 16; no. 5; pp. 1 - 17
Main Authors Slavova, A., Popivanov, P.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2019
Springer Nature B.V
Subjects
Differential equations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Regularity
microlocal solvability
35A18
35H20
involutive and involutive–symplectic characteristics
Hypoellipticity
35A20
subellipticity
Secondary 35H10
Primary 35A27
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Summary:This paper deals with several classes of pseudo-differential operators with double involutive characteristics as well as operators with double involutive–symplectic characteristics. In the first case, microlocal non-solvability is shown, while in the second case, the conditions imposed on the subprincipal symbol are the same as the conditions guaranteeing subellipticity of the operators of principal type. The corresponding loss of regularity is 1 + k k + 1 , k ∈ N . At the end of the paper, an inverse operator of a model one with involutive characteristics and non-elliptic subprincipal symbol is constructed into explicit form.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-019-1396-9