Task mapping, which basically consists of mapping a set of tasks onto a set of nodes, is a well-known problem in distributed computing research. As a particular case of distributed systems, the Internet of Things (IoT) poses a set of renewed challenges, because of its scale, heterogeneity and properties traditionally associated with wireless sensor networks (WSN), shared sensing, continous processing and real time computing. To handle IoT features, we present a formalization of the task mapping problem that captures the varying consumption of resources and various constraints (location, capabilities, QoS) in order to compute a mapping that guarantees the lifetime of the concurrent tasks inside the network and the fair allocation of tasks among the nodes. It results in a binary programming problem for which we provide an efficient heuristic that allows its resolution in polynomial time. Our experiments show that our heuristic: (i) gives solutions that are close to optimal and (ii) can be implemented on reasonably powerful Things and performed directly within the network, without requiring any centralized infrastructure.