In the unsupervised domain adaptation (UDA) depth estimation task, a new adaptive approach is to use the bidirectional transformation network to transfer the style between the target and source domain inputs, and then train the depth estimation network in their respective domains. However, the domain adaptation process and the style transfer may result in defects and biases.Especially in outdoor environments with long distances and complex surroundings, it often leads to map holes and missing areas in the target domain's depth output. To address these issues, We propose a training network that has been improved in terms of model structure and supervision constraints. First, we introduce a edge-guided self-attention mechanism in the task network of each domain to enhance the network's attention to high-frequency edge features, maintain clear boundaries and fill in missing areas of depth. Furthermore, we utilize an edge detection algorithm to extract edge features from the input of the target domain. Then we establish edge consistency constraints between inter-domain entities in order to narrow the gap between domains and make domain-to-domain transfers easier. Our experimental demonstrate that our proposed method effectively solve the aforementioned problem, resulting in a higher quality depth map and outperforming existing state-of-the-art methods.Our code and datasets are all open-sourced at the following address:https://github.com/chongagp/UDA-depth-estimation-under-intra-domain-self-attention-guidance-and-cross-domain-edge-constraints