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On the solvability of pseudodifferential operators

Dencker, Nils LU (2006) Seminaire: Equations aux Dérivées Partielles In Seminaire: Equations aux Dérivées Partielles. 2005--2006 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.
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Nirenberg-Treves conjecture, solvability, principal type, peudodifferential operators
in
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
ISBN
2-7302-1335-X
language
English
LU publication?
yes
id
6eade80b-c19d-435c-8f76-8134a44f6975 (old id 794862)
date added to LUP
2007-12-27 16:58:50
date last changed
2016-10-12 13:29:38
@misc{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},
  isbn         = {2-7302-1335-X},
  keyword      = {Nirenberg-Treves conjecture,solvability,principal type,peudodifferential operators},
  language     = {eng},
  pages        = {29},
  publisher    = {ARRAY(0x890aab0)},
  series       = {Seminaire: Equations aux Dérivées Partielles. 2005--2006},
  title        = {On the solvability of pseudodifferential operators},
  volume       = {1},
  year         = {2006},
}