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Solvability of subprincipal type operators

Dencker, Nils LU (2018) 11th International Society for Analysis, its Applications and Computation, ISAAC 2017 262. p.1-49
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 Σ2. We shall assume that the operator is of subprincipal type, which means that the kth inhomogeneous blowup at Σ2 of the refined principal symbol is of principal type with Hamilton vector field parallel to the base Σ2, but transversal to the symplectic leaves of Σ2 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 Σ2, 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 Σ2. We shall assume that the operator is of subprincipal type, which means that the kth inhomogeneous blowup at Σ2 of the refined principal symbol is of principal type with Hamilton vector field parallel to the base Σ2, but transversal to the symplectic leaves of Σ2 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 Σ2, 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.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Mathematical Analysis and Applications-Plenary 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
2017-08-14 - 2017-08-18
external identifiers
  • scopus:85056874691
ISBN
9783030008734
DOI
10.1007/978-3-030-00874-1_1
language
English
LU publication?
yes
id
0d18aa67-2905-4b82-8dbd-44f2c85ae29c
date added to LUP
2018-11-29 14:36:54
date last changed
2019-02-20 11:38:24
@inproceedings{0d18aa67-2905-4b82-8dbd-44f2c85ae29c,
  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        = {1--49},
  publisher    = {Springer New York LLC},
  title        = {Solvability of subprincipal type operators},
  url          = {http://dx.doi.org/10.1007/978-3-030-00874-1_1},
  volume       = {262},
  year         = {2018},
}