The solvability and subellipticity of systems of pseudodifferential operators
(2009) Siena workshop in honor of Ferruccio Colombini on the occasion of his 60th birthday, 2007 In Progress in Nonlinear Differential Equations and Their Applications 78. p.73-94- Abstract
The paper studies the local solvability and subellipticity for square systems of principal type. These are the systems for which the principal symbol vanishes of first order on its kernel. For systems of principal type having constant characteristics, local solvability is equivalent to condition (Ψ) on the eigenvalues. This is a condition on the sign changes of the imaginary part along the oriented bicharacteristics of the real part of the eigenvalue. In the generic case when the principal symbol does not have constant characteristics, condition (Ψ) is not sufficient and in general not well defined. Instead we study systems which are quasi-symmetrizable, these systems have natural invariance properties and are of principal type. We... (More)
The paper studies the local solvability and subellipticity for square systems of principal type. These are the systems for which the principal symbol vanishes of first order on its kernel. For systems of principal type having constant characteristics, local solvability is equivalent to condition (Ψ) on the eigenvalues. This is a condition on the sign changes of the imaginary part along the oriented bicharacteristics of the real part of the eigenvalue. In the generic case when the principal symbol does not have constant characteristics, condition (Ψ) is not sufficient and in general not well defined. Instead we study systems which are quasi-symmetrizable, these systems have natural invariance properties and are of principal type. We prove that quasi-symmetrizable systems are locally solvable. We also study the subellipticity of quasi-symmetrizable systems in the case when principal symbol vanishes of finite order along the bicharacteristics. In order to prove subellipticity, we assume that the principal symbol has the approximation property, which implies that there are no transversal bicharacteristics.
(Less)
- author
- Dencker, Nils LU
- organization
- publishing date
- 2009-08-21
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Principal type, Pseudodifferential, Solvability, Subelliptic, System
- host publication
- Advances in Phase Space Analysis of Partial Differential Equations - In Honor of Ferruccio Colombini's 60th Birthday
- series title
- Progress in Nonlinear Differential Equations and Their Applications
- editor
- Del Santo, Daniele ; Murthy, M.K. Venkatesha and Bove, Antonio
- volume
- 78
- pages
- 22 pages
- publisher
- Springer
- conference name
- Siena workshop in honor of Ferruccio Colombini on the occasion of his 60th birthday, 2007
- conference location
- Siena, Italy
- conference dates
- 2007-10-10 - 2007-10-13
- external identifiers
-
- scopus:84877910155
- ISSN
- 1421-1750
- 2374-0280
- ISBN
- 9780817648602
- DOI
- 10.1007/978-0-8176-4861-9_5
- language
- English
- LU publication?
- yes
- id
- fff2fb03-1275-4f64-baae-b9c3ba6f3139
- date added to LUP
- 2019-06-24 10:49:47
- date last changed
- 2024-01-01 12:34:49
@inproceedings{fff2fb03-1275-4f64-baae-b9c3ba6f3139,
abstract = {{<p>The paper studies the local solvability and subellipticity for square systems of principal type. These are the systems for which the principal symbol vanishes of first order on its kernel. For systems of principal type having constant characteristics, local solvability is equivalent to condition (Ψ) on the eigenvalues. This is a condition on the sign changes of the imaginary part along the oriented bicharacteristics of the real part of the eigenvalue. In the generic case when the principal symbol does not have constant characteristics, condition (Ψ) is not sufficient and in general not well defined. Instead we study systems which are quasi-symmetrizable, these systems have natural invariance properties and are of principal type. We prove that quasi-symmetrizable systems are locally solvable. We also study the subellipticity of quasi-symmetrizable systems in the case when principal symbol vanishes of finite order along the bicharacteristics. In order to prove subellipticity, we assume that the principal symbol has the approximation property, which implies that there are no transversal bicharacteristics.</p>}},
author = {{Dencker, Nils}},
booktitle = {{Advances in Phase Space Analysis of Partial Differential Equations - In Honor of Ferruccio Colombini's 60th Birthday}},
editor = {{Del Santo, Daniele and Murthy, M.K. Venkatesha and Bove, Antonio}},
isbn = {{9780817648602}},
issn = {{1421-1750}},
keywords = {{Principal type; Pseudodifferential; Solvability; Subelliptic; System}},
language = {{eng}},
month = {{08}},
pages = {{73--94}},
publisher = {{Springer}},
series = {{Progress in Nonlinear Differential Equations and Their Applications}},
title = {{The solvability and subellipticity of systems of pseudodifferential operators}},
url = {{http://dx.doi.org/10.1007/978-0-8176-4861-9_5}},
doi = {{10.1007/978-0-8176-4861-9_5}},
volume = {{78}},
year = {{2009}},
}