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The proof of the Nirenberg-Treves conjecture

Dencker, Nils LU (2003) Journées "Équations aux Dérivées Partielles" In 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).
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
principal type, Nirenberg-Treves conjecture, pseudodifferential operators, solvability
in
Journées "Équations aux Dérivées Partielles"
pages
25 pages
publisher
Univ. Nantes, Nantes, France
conference name
Journées "Équations aux Dérivées Partielles"
ISBN
2-86939-207-9
language
English
LU publication?
yes
id
46f17bda-e387-4964-a3c9-fff1f06d7e00 (old id 794908)
date added to LUP
2007-12-27 17:04:18
date last changed
2016-10-12 13:29:38
@misc{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},
  isbn         = {2-86939-207-9},
  keyword      = {principal type,Nirenberg-Treves conjecture,pseudodifferential operators,solvability},
  language     = {eng},
  pages        = {25},
  publisher    = {ARRAY(0x9359730)},
  series       = {Journées "Équations aux Dérivées Partielles"},
  title        = {The proof of the Nirenberg-Treves conjecture},
  year         = {2003},
}