Analytic Hypoellipticity in the Presence of Lower Order Terms

2006/03/14 by Paolo Albano, Paolo G. Albano, Albano, Paolo +4
Mathematics · Physics and Astronomy · #35H10 #35N15 #Advanced Differential Geometry Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.AP #msc:35H10 #msc:35N15

paper · pdf · doi:10.48550/arxiv.math/0603317

40 pages

openalex publication_date 2006/03/14 · arxiv created 2006/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a second order operator with analytic coefficients whose principal symbol vanishes exactly to order two on a symplectic real analytic manifold. We assume that the first (non degenerate) eigenvalue vanishes on a symplectic submanifold of the characteristic manifold. In the C^∞ framework this situation would mean a loss of 3/2 derivatives. We prove that this operator is analytic hypoelliptic. The main tool is the FBI transform. A case in which C^∞ hypoellipticity fails is also discussed.

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