The proof of the Nirenberg-Treves conjecture
(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:
https://lup.lub.lu.se/record/794908
- author
- Dencker, Nils LU
- organization
- publishing date
- 2003
- 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}}, }