Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

The proof of the Nirenberg-Treves conjecture

Dencker, Nils LU (2003) Journées "Équations aux Dérivées Partielles"
Abstract
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).
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
principal type, Nirenberg-Treves conjecture, pseudodifferential operators, solvability
host publication
Journées "Équations aux Dérivées Partielles"
pages
25 pages
publisher
Univ. Nantes, Nantes, France
conference name
Journées "Équations aux Dérivées Partielles"
conference location
Forges-les-Eaux, France
conference dates
2003-06-02
ISBN
2-86939-207-9
language
English
LU publication?
yes
id
46f17bda-e387-4964-a3c9-fff1f06d7e00 (old id 794908)
date added to LUP
2016-04-04 11:09:59
date last changed
2018-11-21 21:03:04
@inproceedings{46f17bda-e387-4964-a3c9-fff1f06d7e00,
  abstract     = {{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).}},
  author       = {{Dencker, Nils}},
  booktitle    = {{Journées "Équations aux Dérivées Partielles"}},
  isbn         = {{2-86939-207-9}},
  keywords     = {{principal type; Nirenberg-Treves conjecture; pseudodifferential operators; solvability}},
  language     = {{eng}},
  publisher    = {{Univ. Nantes, Nantes, France}},
  title        = {{The proof of the Nirenberg-Treves conjecture}},
  year         = {{2003}},
}