Solvability of subprincipal type operators
(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.
(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 Applications-Plenary Lectures - ISAAC 2017
- editor
- Toft, Joachim and Rodino, Luigi G.
- volume
- 262
- pages
- 49 pages
- publisher
- Springer
- 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
- 2022-01-31 07:33:43
@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}}, booktitle = {{Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017}}, editor = {{Toft, Joachim and Rodino, Luigi G.}}, isbn = {{9783030008734}}, language = {{eng}}, pages = {{1--49}}, publisher = {{Springer}}, title = {{Solvability of subprincipal type operators}}, url = {{http://dx.doi.org/10.1007/978-3-030-00874-1_1}}, doi = {{10.1007/978-3-030-00874-1_1}}, volume = {{262}}, year = {{2018}}, }