Udett Schaffrath from Computer Bild has published a video, proving that the DualShock 4 works on the PS3. However, the controller doesn't work with every game, and it requires to be pluged on the PS3 in order to work.
In the video, Schaffrath made his first test with Urban Trial Freestyle, showing that the controller worked perfectly with the game. Soon after this demonstration, he revealed that he had tried playing FIFA 14, however the controller wouldn't work beyond the game's menus.
Sony had previously revealed that the PS4's controller would be compatible with PC, so it might be possible that the company is planning to have the PS3 have full compability with DualShock 4. The PS4 will be released on the 15th of November in North America, arriving at Europe two weeks later, on the 29th of November.