Recently, Dynamic Adaptive Streaming over HTTP (DASH) has attracted significant attention. In this paper, we consider DASH-based transmission of scalable videos in wireless broadband access networks (e.g., long-term evolution and WiMAX), and propose three methods to enhance the quality of experience of wireless DASH users. First, we design an improved mapping scheme from scalable video coding layers to DASH layers that can provide the desired bitrates, enhance the video end-to-end throughput, and reduce the HTTP communication overhead. Second, we develop a DASH-friendly scheduling and resource allocation algorithm by integrating the DASH-based media delivery and the radio-level adaptation via a cross-layer approach. It utilizes the characteristics of video content and scalable video coding, and greatly reduces the possibility of video playback interruption by considering the client buffer status. The optimization problem is formulated as a mixed binary integer programming problem, and is solved by a subgradient method. Finally, a DASH proxy-based bitrate stabilization algorithm is proposed to improve the video playback smoothness that can achieve the desired tradeoff between playback quality and stability. Simulations with the Qualnet tool demonstrate that our schemes achieve better performances than other methods in the literature.