We aim at finding optimal mappings for concurrent streaming applications. Each application consists of a linear chain with several stages, and processes successive data sets in pipeline mode. The objective is to minimize the energy consumption of the whole platform, while satisfying given performance-related bounds on the period and latency of each application. The problem is to decide which processors to enroll, at which speed (or mode) to use them, and which stages they should execute. Processors can be identical (with the same modes) or heterogeneous. We also distinguish two mapping categories, interval mappings, and general mappings. For interval mappings, a processor is assigned a set of consecutive stages of the same application, so there is no resource sharing across applications. On the contrary, the assignment is fully arbitrary for general mappings, hence a processor can be reused for several applications. On the theoretical side, we establish complexity results for this tri-criteria mapping problem (energy, period, latency), classifying polynomial versus NP-complete instances. Furthermore, we derive an integer linear program that provides the optimal solution in the most general case. On the experimental side, we design polynomial-time heuristics, and assess their absolute performance thanks to the linear program. One main goal is to assess the impact of processor sharing on the quality of the solution.