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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.

35A21 Singularity in context of PDEs
35H10 Hypoelliptic equations
35B65 Smoothness and regularity of solutions to PDEs
Full Text: DOI
[1] Baouendi , M. S. , Trèves , F. ( 1981 ).A Local Constancy Principle for the Solutions of Certain Overdetermined Systems of First-Order Linear Partial Differential Equations. Adv. in Math. Suppl. Stud., 7a , New York-London : Academic Press , pp. 245 – 262 . · Zbl 0475.35027
[2] DOI: 10.1512/iumj.1982.31.31060 · Zbl 0505.32013 · doi:10.1512/iumj.1982.31.31060
[3] DOI: 10.1090/S0002-9947-99-02299-0 · Zbl 0932.35046 · doi:10.1090/S0002-9947-99-02299-0
[4] DOI: 10.1006/jfan.1993.1068 · Zbl 0777.58041 · doi:10.1006/jfan.1993.1068
[5] Bergamasco A., Mat. Contemp. 18 pp 43– (2000)
[6] DOI: 10.1016/S0022-1236(02)00055-1 · Zbl 1034.32024 · doi:10.1016/S0022-1236(02)00055-1
[7] DOI: 10.1090/S0002-9947-05-03905-X · Zbl 1077.35004 · doi:10.1090/S0002-9947-05-03905-X
[8] Cartan H., Bull. Soc. Math. France 85 pp 77– (1957)
[9] DOI: 10.2307/1970257 · Zbl 0108.07804 · doi:10.2307/1970257
[10] DOI: 10.1090/S0002-9939-1972-0301459-3 · doi:10.1090/S0002-9939-1972-0301459-3
[11] Malgrange B., Bull. Soc. Math. France 85 pp 231– (1957)
[12] Treves F., Hypo-Analytic Structures (1992) · Zbl 0787.35003
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