Mobility in 6LoWPAN (IPv6 over Low Power Personal Area Networks) is being utilized in realizing many applications where sensor nodes, while moving, sense and transmit the gathered data to a monitoring server. By employing IEEE802.15.4 as a baseline for the link layer technology, 6LoWPAN implies low data rate and low power consumption with periodic sleep and wakeups for sensor nodes, without requiring them to incorporate complex hardware. Also enabling sensor nodes with IPv6 ensures that the sensor data can be accessed anytime and anywhere from the world. Several existing mobility-related schemes like HMIPv6, MIPv6, HAWAII, and Cellular IP require active participation of mobile nodes in the mobility signaling, thus leading to the mobility-related changes in the protocol stack of mobile nodes. In this paper, we present LoWMob, which is a network-based mobility scheme for mobile 6LoWPAN nodes in which the mobility of 6LoWPAN nodes is handled at the network-side. LoWMob ensures multi-hop communication between gateways and mobile nodes with the help of the static nodes within a 6LoWPAN. In order to reduce the signaling overhead of static nodes for supporting mobile nodes, LoWMob proposes a mobility support packet format at the adaptation layer of 6LoWPAN. Also we present a distributed version of LoWMob, named as DLoWMob (or Distributed LoWMob), which employs Mobility Support Points (MSPs) to distribute the traffic concentration at the gateways and to optimize the multi-hop routing path between source and destination nodes in a 6LoWPAN. Moreover, we have also discussed the security considerations for our proposed mobility schemes. The performance of our proposed schemes is evaluated in terms of mobility signaling costs, end-to-end delay, and packet success ratio.