For embedded system software, it is common to use static mappings of tasks to cores. This becomes considerably more challenging in multi-application scenarios. In this paper, we propose TETRiS, a multi-application run-time system for static mappings for heterogeneous system-on-chip architectures. It leverages compile-time information to map and migrate tasks in a fashion that preserves the predictable performance of using static mappings allowing the system to accommodate multiple applications. TETRiS runs on off-the-shelf embedded systems and is Linux-compatible. We embed our approach in a state-of-the-art compiler for multicore systems and evaluate the proposed run-time system in a modern heterogeneous platform using realistic benchmarks. We present two experiments whose execution time and energy consumptions are comparable to those obtained by the highly-optimized Linux scheduler CFS, and where execution time variance is reduced by a factor of 510, and energy consumption variance by a factor of 83.