Solvability of subprincipal type operators

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

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.

Details

Authors
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematical Analysis
Original languageEnglish
Title of host publicationMathematical Analysis and Applications-Plenary Lectures - ISAAC 2017
EditorsJoachim Toft, Luigi G. Rodino
PublisherSpringer
Pages1-49
Number of pages49
Volume262
ISBN (Print)9783030008734
Publication statusPublished - 2018
Publication categoryResearch
Peer-reviewedYes
Event11th International Society for Analysis, its Applications and Computation, ISAAC 2017 - Vaxjo, Sweden
Duration: 2017 Aug 142017 Aug 18

Conference

Conference11th International Society for Analysis, its Applications and Computation, ISAAC 2017
CountrySweden
CityVaxjo
Period2017/08/142017/08/18