Regularity and Solvability of Pseudo-differential Operators with Double Characteristics

  • A. SlavovaEmail author
  • P. Popivanov


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 \( 1+ \frac{k}{k+1} \), \( k \in {\mathbf{N}} \). 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.


Hypoellipticity microlocal solvability subellipticity involutive and involutive–symplectic characteristics 

Mathematics Subject Classification

Primary 35A27 35A20 35A18 Secondary 35H10 35H20 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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