On the solvability of pseudodifferential operators
(2006) Seminaire: Equations aux Dérivées Partielles 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/794862
- author
- Dencker, Nils LU
- organization
- publishing date
- 2006
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Nirenberg-Treves conjecture, solvability, principal type, peudodifferential operators
- host publication
- 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
- conference location
- École Polytechnique, Centre de Mathématiques, Palaiseau, France
- conference dates
- 0001-01-02
- ISBN
- 2-7302-1335-X
- language
- English
- LU publication?
- yes
- id
- 6eade80b-c19d-435c-8f76-8134a44f6975 (old id 794862)
- date added to LUP
- 2016-04-04 11:36:40
- date last changed
- 2018-11-21 21:05:59
@inproceedings{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}}, booktitle = {{Seminaire: Equations aux Dérivées Partielles. 2005--2006}}, isbn = {{2-7302-1335-X}}, keywords = {{Nirenberg-Treves conjecture; solvability; principal type; peudodifferential operators}}, language = {{eng}}, publisher = {{École Polytechnique, Centre de Mathématiques, Palaiseau, France}}, title = {{On the solvability of pseudodifferential operators}}, volume = {{1}}, year = {{2006}}, }