Analytic Hypoellipticity in the Presence of Lower Order Terms

Details Analytic Hypoellipticity in the Presence of Lower Order Terms Analytic Hypoellipticity in the Presence of Lower Order Terms

2006-03-14

arxiv.org/abs/math/0603317v2

Mathematics

Analysis of PDEs

40 pages

Scientific paper

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 $C^\infty$ 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 $C^\infty$ hypoellipticity fails is also discussed.

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