The Wall Street Journal is reporting that Sharp will supply the displays for the new iPad 3 rumoured for release in March of 2012, they state:
"The person also said Apple is also investing in facilities at Sharp’s panel manufacturing factories in Japan, without specifying the amount being invested, highlighting Apple’s plans to work with multiple component makers to ensure that it can secure enough parts to make its popular iPhones and iPads. Osaka-based Sharp makes liquid crystal displays, which are widely used in tablets, smartphones and flat-screen televisions. Sharp already supplies LCD panels for Apple’s iPhone smartphones, according to the person. The company will be supplying panels for the next iPhone, which is also expected to launch sometime next year, the person added."
They also mentioned that Sharp already supplies the displays for the current iPhone 4s. This seems inevitable as Apple's legal battles with Samsung heat up.