# Solvability of subprincipal type operators

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding

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**Solvability of subprincipal type operators.** / Dencker, Nils.

Research output: Chapter in Book/Report/Conference proceeding › Paper in conference proceeding

### Harvard

*Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017.*vol. 262, Springer, pp. 1-49, 11th International Society for Analysis, its Applications and Computation, ISAAC 2017, Vaxjo, Sweden, 2017/08/14. https://doi.org/10.1007/978-3-030-00874-1_1

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*Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017*(Vol. 262, pp. 1-49). Springer. https://doi.org/10.1007/978-3-030-00874-1_1

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*Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017.*Springer. 2018, 1-49. https://doi.org/10.1007/978-3-030-00874-1_1

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### RIS

TY - GEN

T1 - Solvability of subprincipal type operators

AU - Dencker, Nils

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-030-00874-1_1

DO - 10.1007/978-3-030-00874-1_1

M3 - Paper in conference proceeding

SN - 9783030008734

VL - 262

SP - 1

EP - 49

BT - Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017

A2 - Toft, Joachim

A2 - Rodino, Luigi G.

PB - Springer

ER -