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Pseudo-differential operators with multiple characteristics and Gevrey singularities. (English) Zbl 0597.58034

Let A be an analytic pseudo-differential operator whose principal symbol is assumed to vanish exactly at the order \(k\geq 2\) on a regular submanifold of codimension 1 in the cotangent space. Let \(0<p<1\). Then under an appropriate p-Levi condition the authors prove a result of propagation of singularities in the Gevrey class \(G^ s\) with \(1<s<1/p\), construct null solutions with prescribed singularities and give a microlocal existence theorem.
Reviewer: C.Zuily

MSC:

58J40 Pseudodifferential and Fourier integral operators on manifolds
58J47 Propagation of singularities; initial value problems on manifolds
Full Text: DOI

References:

[1] Aoki T, I, II, III, IV, V, Proc. Japan. Acad., Ser. A 58 pp 58– (1982) · Zbl 0507.58039 · doi:10.3792/pjaa.58.58
[2] Bony J.M., Astérisque 34 pp 43– (1976)
[3] DOI: 10.5802/aif.601 · Zbl 0312.35064 · doi:10.5802/aif.601
[4] DOI: 10.5802/aif.429 · Zbl 0235.47029 · doi:10.5802/aif.429
[5] DOI: 10.5802/aif.258 · Zbl 0195.14403 · doi:10.5802/aif.258
[6] Cattabriga L., Applications to the Cauchy problem for hyperbolic operators. pp 2– (1985) · Zbl 0581.35007
[7] Chazarain I.J., Ann. Inst. Fourier, Grenoble 24 pp 209– (1974)
[8] DOI: 10.1007/BF02392165 · Zbl 0232.47055 · doi:10.1007/BF02392165
[9] Egorov J.V., Dokl. Akad. Nauk. SSSR 234 pp 280– (1977)
[10] DOI: 10.1080/03605308308820303 · Zbl 0525.35086 · doi:10.1080/03605308308820303
[11] DOI: 10.1002/cpa.3160240505 · Zbl 0226.35019 · doi:10.1002/cpa.3160240505
[12] Hörmander. 1983. ”The analysis of linear partial differential operators, I, II”. Berlin, Heidelberg: Springer-Verlag. New York, Tokyo
[13] Ivrii V. Ja., Sib. Mat. Zh. 17 pp 547– (1976)
[14] Kessab, A. 1984. Propagation des singularités Gevrey pour des opérateurs à caractéristiques involutives\(title: Th\`ese, Universit\'e de Paris-Sud, Centre d'Orsay. 1984.\)
[15] Komatsu H., J. Fac. Sci. Univ. Tokoyo, Sect 20 pp 25– (1973)
[16] Liess, O. and Rodino, L. A general class of Gevrey type pseudodifferential operators. Journées Equations aux derivées partielles conf. n. 6. 1983. Saint-Jean-de-Monts.
[17] Liess O., Boll. Un. Mat. It., Sez. VI 3 pp 233– (1984)
[18] Mizohata S., J. Vaillant, Université de Paris VI pp 106– (1983)
[19] DOI: 10.5802/aif.602 · Zbl 0313.58021 · doi:10.5802/aif.602
[20] DOI: 10.2977/prims/1195181409 · Zbl 0574.35082 · doi:10.2977/prims/1195181409
[21] Trèves F., I, Plenum Publ. Corp. (1980)
[22] Wakabayashi S., Japan. J. Math. 6 pp 179– (1980)
[23] DOI: 10.3792/pjaa.59.182 · Zbl 0527.35048 · doi:10.3792/pjaa.59.182
[24] Zanghirati L., Pseudodifferential operators of infinite order and Gevrey classes, Ann. Univ. Ferrara, to appear. · Zbl 0601.35110
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