Leichtnam, Eric Interactions de singularités pour une classe d’équations à caractéristiques doubles. (French) Zbl 0553.35090 Ann. Inst. Fourier 35, No. 4, 151-161 (1985). 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. Cited in 2 Documents 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 Keywords:multiple characteristics; Sobolev spaces; propagation of singularities; pseudo-differential operators; nonlinear; parametrices Citations:Zbl 0446.35087 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] [1] , 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] [2] , , Au-delà des opérateurs pseudo-différentiels, Astérisque, vol. 57 (1978). · Zbl 0483.35082 [3] [3] , 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).0224.3508448 #9458 · Zbl 0224.35084 [5] V. IVRII, Sufficient conditions for regular and completely regular hyperbolicity, Trans. Moscow Math. Soc., issue 1 (1978).0376.35038 · Zbl 0376.35038 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.