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The question of solvability

Dencker, Nils LU (2003) Hyperbolic problems and related topics p.159-184
Abstract
We give a 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 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
pseudodifferential operators, Nirenberg-Treves conjecture, solvability, principal type
host publication
Graduate Series in Analysis
editor
Colombini, Ferruccio ; Nishitani, Tatsuo ; and
pages
26 pages
publisher
International Press, Somerville, MA, USA
conference name
Hyperbolic problems and related topics
conference location
Cortona, Italy
conference dates
2002-09-10
ISBN
1-57146-150-7
language
English
LU publication?
yes
id
a19f5fb2-c3f7-461d-b11d-f992cf79c11f (old id 795053)
date added to LUP
2016-04-04 10:30:15
date last changed
2018-11-21 20:59:09
@inproceedings{a19f5fb2-c3f7-461d-b11d-f992cf79c11f,
  abstract     = {We give a 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 two derivatives (compared with the elliptic case).},
  author       = {Dencker, Nils},
  booktitle    = {Graduate Series in Analysis},
  editor       = {Colombini, Ferruccio and Nishitani, Tatsuo},
  isbn         = {1-57146-150-7},
  language     = {eng},
  pages        = {159--184},
  publisher    = {International Press, Somerville, MA, USA},
  title        = {The question of solvability},
  year         = {2003},
}