The question of solvability
(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).
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/795053
- author
- Dencker, Nils LU
- organization
- publishing date
- 2003
- 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 and Nishitani, Tatsuo
- 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}}, keywords = {{pseudodifferential operators; Nirenberg-Treves conjecture; solvability; principal type}}, language = {{eng}}, pages = {{159--184}}, publisher = {{International Press, Somerville, MA, USA}}, title = {{The question of solvability}}, year = {{2003}}, }