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Solvability and limit bicharacteristics

Dencker, Nils LU (2016) In Journal of Pseudo-Differential Operators and Applications 7(3). p.295-320
Abstract

We study the solvability of pseudodifferential operators which are not of principal type. The operator will have real principal symbol and we shall consider the limits of bicharacteristics at the set where the principal symbol vanishes of at least second order. The convergence shall be as smooth curves, then the limit bicharacteristic also is a smooth curve. We shall also need uniform bounds on the curvature of the characteristics at the bicharacteristics, but only along the tangents of a given Lagrangean manifold. This gives uniform bounds on the linearization of the normalized Hamilton flow on the tangent space of this manifold at the bicharacteristics. If the quotient of the imaginary part of the subprincipal symbol with the norm of... (More)

We study the solvability of pseudodifferential operators which are not of principal type. The operator will have real principal symbol and we shall consider the limits of bicharacteristics at the set where the principal symbol vanishes of at least second order. The convergence shall be as smooth curves, then the limit bicharacteristic also is a smooth curve. We shall also need uniform bounds on the curvature of the characteristics at the bicharacteristics, but only along the tangents of a given Lagrangean manifold. This gives uniform bounds on the linearization of the normalized Hamilton flow on the tangent space of this manifold at the bicharacteristics. If the quotient of the imaginary part of the subprincipal symbol with the norm of the Hamilton vector field switches sign from − to + on the bicharacteristics and becomes unbounded as they converge to the limit, then the operator is not solvable at the limit bicharacteristic.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Limit bicharacteristic, Pseudodifferential operator, Solvability, Subprincipal symbol
in
Journal of Pseudo-Differential Operators and Applications
volume
7
issue
3
pages
26 pages
publisher
Birkhaeuser Verlag AG
external identifiers
  • scopus:84979732852
  • wos:000380273500001
ISSN
1662-9981
DOI
10.1007/s11868-016-0164-x
language
English
LU publication?
yes
id
dc20989e-0dad-44a3-b9b3-17b76694fc2c
date added to LUP
2016-11-11 14:50:49
date last changed
2017-09-24 05:03:02
@article{dc20989e-0dad-44a3-b9b3-17b76694fc2c,
  abstract     = {<p>We study the solvability of pseudodifferential operators which are not of principal type. The operator will have real principal symbol and we shall consider the limits of bicharacteristics at the set where the principal symbol vanishes of at least second order. The convergence shall be as smooth curves, then the limit bicharacteristic also is a smooth curve. We shall also need uniform bounds on the curvature of the characteristics at the bicharacteristics, but only along the tangents of a given Lagrangean manifold. This gives uniform bounds on the linearization of the normalized Hamilton flow on the tangent space of this manifold at the bicharacteristics. If the quotient of the imaginary part of the subprincipal symbol with the norm of the Hamilton vector field switches sign from − to + on the bicharacteristics and becomes unbounded as they converge to the limit, then the operator is not solvable at the limit bicharacteristic.</p>},
  author       = {Dencker, Nils},
  issn         = {1662-9981},
  keyword      = {Limit bicharacteristic,Pseudodifferential operator,Solvability,Subprincipal symbol},
  language     = {eng},
  month        = {09},
  number       = {3},
  pages        = {295--320},
  publisher    = {Birkhaeuser Verlag AG},
  series       = {Journal of Pseudo-Differential Operators and Applications},
  title        = {Solvability and limit bicharacteristics},
  url          = {http://dx.doi.org/10.1007/s11868-016-0164-x},
  volume       = {7},
  year         = {2016},
}