Solvability and limit bicharacteristics
(2016) In Journal of PseudoDifferential Operators and Applications 7(3). p.295320 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.
(Less)
 author
 Dencker, Nils ^{LU}
 organization
 publishing date
 20160901
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Limit bicharacteristic, Pseudodifferential operator, Solvability, Subprincipal symbol
 in
 Journal of PseudoDifferential Operators and Applications
 volume
 7
 issue
 3
 pages
 26 pages
 publisher
 Birkhaeuser Verlag AG
 external identifiers

 scopus:84979732852
 wos:000380273500001
 ISSN
 16629981
 DOI
 10.1007/s118680160164x
 language
 English
 LU publication?
 yes
 id
 dc20989e0dad44a3b9b317b76694fc2c
 date added to LUP
 20161111 14:50:49
 date last changed
 20170924 05:03:02
@article{dc20989e0dad44a3b9b317b76694fc2c, 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 = {16629981}, keyword = {Limit bicharacteristic,Pseudodifferential operator,Solvability,Subprincipal symbol}, language = {eng}, month = {09}, number = {3}, pages = {295320}, publisher = {Birkhaeuser Verlag AG}, series = {Journal of PseudoDifferential Operators and Applications}, title = {Solvability and limit bicharacteristics}, url = {http://dx.doi.org/10.1007/s118680160164x}, volume = {7}, year = {2016}, }