On the solvability of pseudodifferential operators
Författare
Summary, in English
We give a new proof of the Nirenberg-Treves conjecture: that local solvability of principal type pseudodifferential operators is equivalent to condition (Psi). This condition rules out sign changes from - to + of the imaginary part of the principal symbol along the oriented bicharacteristics of the real part. We obtain local solvability by proving a localizable a priori estimate for the adjoint operator with a loss of 3/2 derivatives (compared with the elliptic case), using some ideas of Nicolas Lerner.
Avdelning/ar
- Matematik (naturvetenskapliga fakulteten)
- Partial differential equations
Publiceringsår
2006
Språk
Engelska
Publikation/Tidskrift/Serie
Seminaire: Equations aux Dérivées Partielles. 2005--2006
Volym
1
Dokumenttyp
Konferensbidrag
Förlag
École Polytechnique, Centre de Mathématiques, Palaiseau, France
Ämne
- Mathematics
Nyckelord
- Nirenberg-Treves conjecture
- solvability
- principal type
- peudodifferential operators
Conference name
Seminaire: Equations aux Dérivées Partielles
Conference date
0001-01-02
Conference place
École Polytechnique, Centre de Mathématiques, Palaiseau, France
Status
Published
Forskningsgrupp
- Partial differential equations
ISBN/ISSN/Övrigt
- ISBN: 2-7302-1335-X