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Global analytic regularity for structures of co-rank one. (English) Zbl 1153.35006
The authors consider a real analytic involutive structure \({\mathcal V}\), of co-rank one, defined on a real analytic paracompact orientable manifold \(M\). To such a structure certain connected sets (called level sets of \({\mathcal V}\)) are associated. The authors prove that analytic regularity propagates along them. With further assumptions on the level sets the global analytic hypoellipticity of a differential operator naturally associated to \({\mathcal V}\) is characterized. An application is given to the case of tube structures.

MSC:
35A21 Singularity in context of PDEs
35H10 Hypoelliptic equations
35B65 Smoothness and regularity of solutions to PDEs
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