## 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

Zbl 0446.35087
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### References:

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