A 19-year-old inmate was stabbed at a Milpitas jail Saturday, authorities said today. The victim, who has been in custody for less than a month on charges of burglary, possession of stolen property and tampering with a vehicle, was exercising with several other inmates in a medium security unit at the Elmwood Correctional Facility when he was assaulted at about 7:30 p.m., authorities said. He was transported to Valley Medical Center with a wound to his back and is expected to survive, according to jail officials. A sharpened piece of metal is believed to be the weapon. The Santa Clara County Sheriff’s Department and Department of Correction are investigating the incident.