This stuff should work for you.
It call "GameSwitch" and designed for PS3 displayed in DVI monitor or LCD
http://www.green-box.com.tw/products/view/id/104
GAMESWITCH
Play PlayStation? 3 on a DVI Monitor
Introduction
Play PS3 on a DVI monitor is not a dream anymore! GAMESWITCH makes it become reality. It allows you to play PS3 on a regular DVI monitor, plus its switch function, you can either play PS3 or operate PC. You can play 1080p high quality game on a DVI monitor through GAMESWITCH and don?t have to play on expensive HDMI enabled LCD TV only. Now enjoy PS3 not only in living room, but also besides your PC !
Features
1. Switch PlayStation? 3 and one DVI displayed PC to one DVI monitor and stereo speaker
2. Support 480i, 480p, 720p, 1080i, 1080p
3. Compliant with DVI 1.0
4. Auto and manual channel selection, an external button is attached
5. Electronic design
6. LED status to indicate the source displayed
7. Magnetic pad and attachable metal plate to ease the installation
Connection
http://www.green-box.com.tw/images/illus_ps3_s201.gif
Media Review in GAMER
http://gnn.gamer.com.tw/2/25732.html
Some Test Pictures of Game Switch
20" DVI LCD Monitor(ACER AL2032W) 1920x1080@60Hz (1080p) *Ridge Racer 7*
http://www.jpegr.com/uploads/1/G01.jpg
http://www.jpegr.com/uploads/1/G02.jpg
http://www.jpegr.com/uploads/1/G03.jpg
20" DVI LCD Monitor(ACER AL2032W) 1920x1080@60Hz (1080p) *Ultraviolet* Blu-ray Disc
http://www.jpegr.com/uploads/1/M01.jpg
http://www.jpegr.com/uploads/1/M02.jpg
http://www.jpegr.com/uploads/1/M03.jpg
The monitors can support 1080p over GameSwitch:
Asus 20", Dell 24", Acer 20", LG 20", ViewSonic 19"
Apple monitor is not suggested to use in this situation. Other brands should at least reach 720p.
Above is the information I collected, hope it helps...