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Interactions de singularités pour une classe d’équations à caractéristiques doubles. (French) Zbl 0553.35090

We precise, in Sobolev spaces, the results concerning propagation of singularities obtained by N. Hanges [Ann. Math. Stud. 91, 113-126 (1978; Zbl 0446.35087)] in the \(C^{\infty}\) case for pseudo- differential opertors whose principal symbol is real and whose characteristic variety is the union of two smooth hypersurfaces with noninvolutive intersection. We also obtain a result in a nonlinear case. We prove our results by studying the action of Hanges’s parametrices in Sobolev spaces.

MSC:

35S05 Pseudodifferential operators as generalizations of partial differential operators
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35A20 Analyticity in context of PDEs

Citations:

Zbl 0446.35087
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References:

[1] J.-M. BONY, Calcul symbolique et propagation des singularités pour LES équations aux dérivées partielles non linéaires, Ann. Scient. Ec. Norm. Sup., 4e série, t. 14 (1981). · Zbl 0495.35024
[2] R. COIFMAN, Y. MEYER, Au-delà des opérateurs pseudo-différentiels, Astérisque, vol. 57 (1978). · Zbl 0483.35082
[3] N. HANGES, Parametrices and propagation of singularities for operators with non-involutive characteristics, Indiana University, Math. Journal, vol. 28, N° 1 (1979). · Zbl 0413.35073
[4] L. HORMANDER, On the existence and the regularity of solutions of linear pseudo-differential equations, Ens. Math., 17 (1971). · Zbl 0224.35084
[5] V. IVRII, Sufficient conditions for regular and completely regular hyperbolicity, Trans. Moscow Math. Soc., issue 1 (1978). · Zbl 0376.35038
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