Final answer:
The solution is to use a single VLAN with a flat IP subnet managed by a central controller, allowing for seamless client mobility across different segments without IP address changes.
Step-by-step explanation:
The solution for maintaining connectivity for mobile clients when roaming between different segments in a segmented wireless local area network (LAN) with different Internet Protocol (IP) addresses for each segment is to employ a unified virtual local area network (VLAN) approach. By configuring all access points to operate on a single VLAN using a flat IP subnet, mobile devices can move across different segments without the need to change their IP address. This setup typically involves a central controller that manages traffic and enables seamless mobility for the clients.