System Architecture Evolution (SAE) with Long Term Evolution (LTE) has been used as the key technology for the next generation mobile networks. To support mobility in the LTE/SAE-based mobile networks, the Proxy Mobile IPv6 (PMIP), in which the Mobile Access Gateway (MAG) of the PMIP is deployed at the Serving Gateway (S-GW) of LTE/SAE and the Local Mobility Anchor (LMA) of PMIP is employed at the PDN Gateway (P-GW) of LTE/SAE, is being considered. In the meantime, the Host Identity Protocol (HIP) and the Locator Identifier Separation Protocol (LISP) have recently been proposed with the identifier-locator separation principle, and they can be used for mobility management over the global-scale networks. In this paper, we discuss how to provide the inter-domain mobility management over PMIP-based LTE/SAE networks by investigating three possible scenarios: mobile IP with PMIP (denoted by MIP-PMIP-LTE/SAE), HIP with PMIP (denoted by HIP-PMIP-LTE/SAE), and LISP with PMIP (denoted by LISP-PMIP-LTE/SAE). For performance analysis of the candidate inter-domain mobility management schemes, we analyzed the traffic overhead at a central agent and the total transmission delay required for control and data packet delivery. From the numerical results, we can see that HIP-PMIP-LTE/SAE and LISP-PMIP-LTE/SAE are preferred to MIP-PMIP-LTE/SAE in terms of traffic overhead; whereas, LISP-PMIP-LTE/SAE is preferred to HIP-PMIP-LTE/SAE and MIP-PMIP-LTE/SAE in the viewpoint of total transmission delay.