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On the solvability of pseudodifferential operators

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Author

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.

Department/s

Publishing year

2006

Language

English

Publication/Series

Seminaire: Equations aux Dérivées Partielles. 2005--2006

Volume

1

Document type

Conference paper

Publisher

École Polytechnique, Centre de Mathématiques, Palaiseau, France

Topic

  • Mathematics

Keywords

  • 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

Research group

  • Partial differential equations

ISBN/ISSN/Other

  • ISBN: 2-7302-1335-X