The University of Louisville trustees served notice that they are near a deal with a health-care provider that would be its partner and share the cost and management of its vast health-care operations, including the financially stressed University Hospital, the community's chief safety-net facility. At a meeting Thursday, the trustees gave Dr. David Dunn, the U of L executive vice president for health affairs, the authority to negotiate and sign a final agreement with an undisclosed health-care company—without having to bring the deal back to the trustees for a final endorsement.