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On the solvability of pseudodifferential operators

Dencker, Nils LU (2006) Seminaire: Equations aux Dérivées Partielles 1.
Abstract
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.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Nirenberg-Treves conjecture, solvability, principal type, peudodifferential operators
host publication
Seminaire: Equations aux Dérivées Partielles. 2005--2006
volume
1
pages
29 pages
publisher
École Polytechnique, Centre de Mathématiques, Palaiseau, France
conference name
Seminaire: Equations aux Dérivées Partielles
conference location
École Polytechnique, Centre de Mathématiques, Palaiseau, France
conference dates
0001-01-02
ISBN
2-7302-1335-X
language
English
LU publication?
yes
id
6eade80b-c19d-435c-8f76-8134a44f6975 (old id 794862)
date added to LUP
2016-04-04 11:36:40
date last changed
2018-11-21 21:05:59
@inproceedings{6eade80b-c19d-435c-8f76-8134a44f6975,
  abstract     = {{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.}},
  author       = {{Dencker, Nils}},
  booktitle    = {{Seminaire: Equations aux Dérivées Partielles. 2005--2006}},
  isbn         = {{2-7302-1335-X}},
  keywords     = {{Nirenberg-Treves conjecture; solvability; principal type; peudodifferential operators}},
  language     = {{eng}},
  publisher    = {{École Polytechnique, Centre de Mathématiques, Palaiseau, France}},
  title        = {{On the solvability of pseudodifferential operators}},
  volume       = {{1}},
  year         = {{2006}},
}