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.7394 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 quasisymmetrizable, 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 quasisymmetrizable, these systems have natural invariance properties and are of principal type. We prove that quasisymmetrizable systems are locally solvable. We also study the subellipticity of quasisymmetrizable 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
 20090821
 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
 20071010  20071013
 external identifiers

 scopus:84877910155
 ISSN
 23740280
 14211750
 ISBN
 9780817648602
 DOI
 10.1007/9780817648619_5
 language
 English
 LU publication?
 yes
 id
 fff2fb0312754f64baaeb9c3ba6f3139
 date added to LUP
 20190624 10:49:47
 date last changed
 20210616 06:09:28
@inproceedings{fff2fb0312754f64baaeb9c3ba6f3139, 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 quasisymmetrizable, these systems have natural invariance properties and are of principal type. We prove that quasisymmetrizable systems are locally solvable. We also study the subellipticity of quasisymmetrizable 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 = {23740280}, language = {eng}, month = {08}, pages = {7394}, 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/10.1007/9780817648619_5}, doi = {10.1007/9780817648619_5}, volume = {78}, year = {2009}, }