In previous work, we developed a sound static analysis by abstract interpretation to check the absence of run-time errors in concurrent programs, focusing on embedded C programs composed of a fixed set of threads in a shared memory. The method is thread-modular: it considers each thread independently, analyzing them with respect to an abstraction of the effect of the other threads, so-called interference, which are also inferred automatically as part of analyzing the threads. The analysis thus proceeds in a series of rounds that reanalyze all threads, gathering an increasing set of interference, until stabilization. We proved that this method is sound and covers all possible thread interleavings. This analysis was integrated into the Astrée industrial-scale static analyzer, deployed in avionics and automotive industries. In this article, we consider the more specific case of programs running under a priority-based real-time scheduler, as is often the case in embedded systems. In such programs, higher priority threads cannot be preempted by lower priority ones (except when waiting explicitly for some resource). The programmer exploits this property to reduce the reliance on locks when protecting critical sections. We show how our analysis can be refined through partitioning in order to take into account the real-time hypothesis, remove spurious interleavings, and gain precision on programs that rely on priorities. Our analysis supports in particular dynamic priorities: we handle explicit modifications of the priorities by the program, as well as implicit ones through the priority ceiling protocol. We illustrate our construction formally on an idealized language. Following previous work, we first provide a concrete semantics in thread-modular denotational form that is complete for safety properties, and then show how to apply classic abstractions to obtain an effective static analyzer, able to detect all run-time errors, data-races, as well as deadlocks. Finally, we briefly discuss our implementation inside the Astrée analyzer and ongoing experimentation, with results limited for now to small programs.