Equilibrium conditions for Young measures

Under mild technical assumptions, many nonconvex optimization problems admit generalized solutions where Young measures are used as an accounting device for oscillatory optimal behavior. Once the existence of these generalized solutions is established, the search for optimality conditions that such generalized minimizers must verify is justified. We explore some simple, explicit variational problems where these optimality conditions are obtained, and appropriate manipulation of them leads to the underlying Young measure solution. This in turn encodes the information on how oscillatory behavior minimizes the original optimization problem. This approach may also be relevant with respect to computational issues