REPRESENTATION AND UNIQUENESS FOR BOUNDARY VALUE ELLIPTIC PROBLEMS VIA FIRST ORDER SYSTEMS

Given any elliptic system with t-independent coefficients in the upper- half space, we obtain representation and trace for the conormal gradient of so- lutions in the natural classes for the boundary value problems of Dirichlet and Neumann types with area integral control or non-tangential maximal control. The trace spaces are obtained in a natural range of boundary spaces which is parametrized by properties of some Hardy spaces. This implies a complete picture of uniqueness vs solvability and well-posedness.