Dynamic Adaptive Streaming over HTTP (DASH) has become the standard choice for live events and on-demand video services. In fact, by performing bitrate adaptation at the client side, DASH operates to deliver the highest possible Quality of Experience (QoE) under given network conditions. In cellular networks, in particular, video streaming services are affected by mobility and cell load variation. In this context, DASH video clients continually adapt the streaming quality to cope with channel variability. However, since they operate in a greedy manner, adaptive video clients can overload cellular network resources, degrading the QoE of other users and suffer persistent bitrate oscillations. In this paper, we tackle this problem using a new eNB scheduler, named Shadow-Enforcer, which ensures minimal number of quality switches as well as efficient and fair utilization of network resources. Our scheduler works well under dynamic scenarios and mobility, and requires minimal information, i.e., just the set of video bitrates supported by DASH video clients. It consists of the cascade of a virtual scheduler, Shadow, and the actual scheduler, Enforcer, piloted by the virtual one. Extensive simulations demonstrate the efficiency, fairness and the smooth response to channel variations of the proposed solution.