Advanced

On the Solvability of Systems of Pseudodifferential Operators

Dencker, Nils LU (2008) In Preprint without journal information
Abstract
We study the solvability for a system of pseudodifferential operators. We will assume that the systems is of principal type, i.e., the principal symbol vanishes of first order on the kernel, and that the eigenvalue close to zero has constant multiplicity. We prove that local solvability is to condition (PSI) on the eigenvalues as in the scalar case. This condition rules out any sign changes from

- to + of the imaginary part of the eigenvalue when going in the positive direction on the 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). But we need no conditions on the lower order terms.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
keywords
principal type, systems of pseudodifferential operators, constant characteristics, solvability
in
Preprint without journal information
pages
38 pages
publisher
Manne Siegbahn Institute
external identifiers
  • Other:arXiv:0801.4043
ISSN
0348-7911
language
English
LU publication?
yes
id
789a4d3a-84f2-4c08-956f-4b123a4d7723 (old id 810522)
alternative location
http://www.maths.lth.se/matematiklu/personal/dencker/papers/sysolv.pdf
date added to LUP
2008-03-04 11:51:45
date last changed
2017-02-08 14:45:53
@article{789a4d3a-84f2-4c08-956f-4b123a4d7723,
  abstract     = {We study the solvability for a system of pseudodifferential operators. We will assume that the systems is of principal type, i.e., the principal symbol vanishes of first order on the kernel, and that the eigenvalue close to zero has constant multiplicity. We prove that local solvability is to condition (PSI) on the eigenvalues as in the scalar case. This condition rules out any sign changes from<br/><br>
- to + of the imaginary part of the eigenvalue when going in the positive direction on the 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). But we need no conditions on the lower order terms.},
  author       = {Dencker, Nils},
  issn         = {0348-7911},
  keyword      = {principal type,systems of pseudodifferential operators,constant characteristics,solvability},
  language     = {eng},
  pages        = {38},
  publisher    = {Manne Siegbahn Institute},
  series       = {Preprint without journal information},
  title        = {On the Solvability of Systems of Pseudodifferential Operators},
  year         = {2008},
}