Solvability of subprincipal type operators

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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 vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that P is not solvable.

Detaljer

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Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematisk analys
Originalspråkengelska
Titel på värdpublikationMathematical Analysis and Applications-Plenary Lectures - ISAAC 2017
RedaktörerJoachim Toft, Luigi G. Rodino
FörlagSpringer
Sidor1-49
Antal sidor49
Volym262
ISBN (tryckt)9783030008734
StatusPublished - 2018
PublikationskategoriForskning
Peer review utfördJa
Evenemang11th International Society for Analysis, its Applications and Computation, ISAAC 2017 - Vaxjo, Sverige
Varaktighet: 2017 aug 142017 aug 18

Konferens

Konferens11th International Society for Analysis, its Applications and Computation, ISAAC 2017
LandSverige
OrtVaxjo
Period2017/08/142017/08/18