Solvability of subprincipal type operators
(2018) 11th International Society for Analysis, its Applications and Computation, ISAAC 2017 262. p.149 Abstract
In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order k ≥ 2 at a nonradial involutive manifold Σ_{2}. We shall assume that the operator is of subprincipal type, which means that the kth inhomogeneous blowup at Σ_{2} of the refined principal symbol is of principal type with Hamilton vector field parallel to the base Σ_{2}, but transversal to the symplectic leaves of Σ_{2} at the characteristics. When k = ∞ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of Σ_{2}, and does not satisfying the Nirenberg–Treves condition (Ψ). We also have conditions on the... (More)
In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order k ≥ 2 at a nonradial involutive manifold Σ_{2}. We shall assume that the operator is of subprincipal type, which means that the kth inhomogeneous blowup at Σ_{2} of the refined principal symbol is of principal type with Hamilton vector field parallel to the base Σ_{2}, but transversal to the symplectic leaves of Σ_{2} at the characteristics. When k = ∞ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of Σ_{2}, and does not satisfying the Nirenberg–Treves condition (Ψ). We also have conditions on the vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that P is not solvable.
(Less)
 author
 Dencker, Nils ^{LU}
 organization
 publishing date
 2018
 type
 Chapter in Book/Report/Conference proceeding
 publication status
 published
 subject
 host publication
 Mathematical Analysis and ApplicationsPlenary Lectures  ISAAC 2017
 editor
 Toft, Joachim; Rodino, Luigi G.; and
 volume
 262
 pages
 49 pages
 publisher
 Springer New York LLC
 conference name
 11th International Society for Analysis, its Applications and Computation, ISAAC 2017
 conference location
 Vaxjo, Sweden
 conference dates
 20170814  20170818
 external identifiers

 scopus:85056874691
 ISBN
 9783030008734
 DOI
 10.1007/9783030008741_1
 language
 English
 LU publication?
 yes
 id
 0d18aa6729054b828dbd44f2c85ae29c
 date added to LUP
 20181129 14:36:54
 date last changed
 20190220 11:38:24
@inproceedings{0d18aa6729054b828dbd44f2c85ae29c, abstract = {<p>In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order k ≥ 2 at a nonradial involutive manifold Σ<sub>2</sub>. We shall assume that the operator is of subprincipal type, which means that the kth inhomogeneous blowup at Σ<sub>2</sub> of the refined principal symbol is of principal type with Hamilton vector field parallel to the base Σ<sub>2</sub>, but transversal to the symplectic leaves of Σ<sub>2</sub> at the characteristics. When k = ∞ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of Σ<sub>2</sub>, and does not satisfying the Nirenberg–Treves condition (Ψ). We also have conditions on the vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that P is not solvable.</p>}, author = {Dencker, Nils}, editor = {Toft, Joachim and Rodino, Luigi G.}, isbn = {9783030008734}, language = {eng}, location = {Vaxjo, Sweden}, pages = {149}, publisher = {Springer New York LLC}, title = {Solvability of subprincipal type operators}, url = {http://dx.doi.org/10.1007/9783030008741_1}, volume = {262}, year = {2018}, }