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2017 Operators of subprincipal type
Nils Dencker
Anal. PDE 10(2): 323-350 (2017). DOI: 10.2140/apde.2017.10.323


In this paper we consider the solvability of pseudodifferential operators when the principal symbol vanishes of at least second order at a nonradial involutive manifold Σ2. We shall assume that the subprincipal symbol is of principal type with Hamilton vector field tangent to Σ2 at the characteristics, but transversal to the symplectic leaves of Σ2. We shall also assume that the subprincipal symbol is essentially constant on the leaves of Σ2 and does not satisfying the Nirenberg–Trèves condition (Ψ) on Σ2. In the case when the sign change is of infinite order, we also need a condition on the rate of vanishing of both the Hessian of the principal symbol and the complex part of the gradient of the subprincipal symbol compared with the subprincipal symbol. Under these conditions, we prove that P is not solvable.


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Nils Dencker. "Operators of subprincipal type." Anal. PDE 10 (2) 323 - 350, 2017.


Received: 23 November 2015; Revised: 18 September 2016; Accepted: 1 November 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06693359
MathSciNet: MR3619872
Digital Object Identifier: 10.2140/apde.2017.10.323

Primary: 35S05
Secondary: 35A01 , 47G30 , 58J40

Keywords: pseudodifferential operator , solvability , subprincipal symbol

Rights: Copyright © 2017 Mathematical Sciences Publishers


Vol.10 • No. 2 • 2017
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