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Singular solutions for sums of squares of vector fields. (English) Zbl 0745.35011
The authors investigate two special classes of second order partial differential operators which are sums of squares of smooth vector fields and which are \(C^ \infty\) hypoelliptic at 0. By construction of special solutions it is proven that they are not analytic hypoelliptic at 0. The theorems proposed here generalize or give new proofs of some previous results of Baouendi-Goulaomic, Derridj-Zmily, Helffer, Pham The Lai-Robert, Grigis-Sjöstrand.

MSC:
35H10 Hypoelliptic equations
35A20 Analyticity in context of PDEs
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[1] DOI: 10.1090/S0002-9904-1972-12955-0 · Zbl 0276.35023 · doi:10.1090/S0002-9904-1972-12955-0
[2] DOI: 10.1215/S0012-7094-75-04201-5 · Zbl 0343.35078 · doi:10.1215/S0012-7094-75-04201-5
[3] Christ M., Counterexamples to Analytic Hypoellipticity for Domain of Finite Type Preprint 42 (1990)
[4] DOI: 10.1080/03605308808820586 · Zbl 0736.35070 · doi:10.1080/03605308808820586
[5] Derridj M., 1, in: Comptes Rendus de l’ pp 429– (1988)
[6] Derridj M., Local analyticity for for a class of model doamins not satisfying maximal estiamtes, preprint (1990)
[7] Derridj M., On the Local analyticity in the đ–Neumann problem for some model domains without maximal estiamts preprint. (1990)
[8] Derridj M., J. Math. pures et appl 52 pp 65– (1973)
[9] DOI: 10.2307/2006978 · Zbl 0541.35017 · doi:10.2307/2006978
[10] DOI: 10.1215/S0012-7094-85-05203-2 · Zbl 0581.35009 · doi:10.1215/S0012-7094-85-05203-2
[11] DOI: 10.1016/0022-0396(82)90008-0 · Zbl 0458.35019 · doi:10.1016/0022-0396(82)90008-0
[12] Hörmander, L. 1983. ”The analysis of linear partial differential operators I”. Springer–Verlag. · Zbl 0521.35001
[13] DOI: 10.1007/BF02392081 · Zbl 0156.10701 · doi:10.1007/BF02392081
[14] Kohn J. J., Proceedings of symposia in pure mathematics pp 61– (1973)
[15] DOI: 10.3792/pja/1195519291 · Zbl 0272.47032 · doi:10.3792/pja/1195519291
[16] Matsuzawa T., Nagoya Math. J. 42 pp 43– (1971)
[17] DOI: 10.1512/iumj.1980.29.29059 · Zbl 0455.35041 · doi:10.1512/iumj.1980.29.29059
[18] Metivier G., Comm. in P.D.E 1 pp 1– (1981)
[19] DOI: 10.1090/S0002-9947-1928-1501459-X · doi:10.1090/S0002-9947-1928-1501459-X
[20] DOI: 10.1007/BF02937354 · Zbl 0444.35065 · doi:10.1007/BF02937354
[21] DOI: 10.1007/BF02392419 · Zbl 0346.35030 · doi:10.1007/BF02392419
[22] Sjöstrand J., Hokkaido Mathematical Journal 12 pp 392– (1983)
[23] DOI: 10.1007/BF02414189 · Zbl 0456.35019 · doi:10.1007/BF02414189
[24] DOI: 10.1080/03605307808820074 · Zbl 0384.35055 · doi:10.1080/03605307808820074
[25] DOI: 10.1007/BF01474161 · JFM 41.0343.01 · doi:10.1007/BF01474161
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