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Let D be a bounded strictly pseudoconvex domain with smooth boundary and f = (f1, . . . , fp) (fi [member of] Hol(¯ D)) a complete intersection with normal crossing. In this paper we study an extension problem in L[infinity]-norm for holomorphic functions defined on f-1(0) [intersection] D and a decomposition formula [formula] for holomorphic functions g [member of] I(f1,...,fp)(D) in Lipschitz spaces. We stress that for the two problems the classical theorem cannot be applied because f-1(0) has singularities on the boundary [delta]D. This work is the first step to understand this type of problem in the general singular case

Extension et division dans les variétés à croisements normaux