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The proof of the Nirenberg-Treves conjecture

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Author

Summary, in English

We give a proof of the Nirenberg-Treves conjecture: that local solvability of principal type pseudo-differential 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 two derivatives (compared with the elliptic case).

Department/s

Publishing year

2003

Language

English

Publication/Series

Journées "Équations aux Dérivées Partielles"

Document type

Conference paper

Publisher

Univ. Nantes, Nantes, France

Topic

  • Mathematics

Keywords

  • principal type
  • Nirenberg-Treves conjecture
  • pseudodifferential operators
  • solvability

Conference name

Journées "Équations aux Dérivées Partielles"

Conference date

2003-06-02

Conference place

Forges-les-Eaux, France

Status

Published

Research group

  • Partial differential equations

ISBN/ISSN/Other

  • ISBN: 2-86939-207-9