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The solvability of pseudo-differential operators

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Author

Editor

  • Ferruccio Colombini
  • Ludovico Pernazza

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 arbitrary more than 3/2 derivatives (compared with the elliptic case).

Department/s

Publishing year

2004

Language

English

Pages

175-200

Publication/Series

[Host publication title missing]

Volume

1

Document type

Conference paper

Publisher

Pubbl. Cent. Ric. Mat. Ennio Giorgi

Topic

  • Mathematics

Keywords

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

Conference name

Phase space analysis of partial differential equations

Conference date

0001-01-02

Status

Published

Research group

  • Partial differential equations

ISBN/ISSN/Other

  • ISBN: 88-7642-150-5