Generalized second order vectorial ∞-eigenvalue problems

We consider the problem of minimizing the L-infinity norm of a function of the hessian over a class of maps, subject to a mass constraint involving the L(infinity )norm of a function of the gradient and the map itself. We assume zeroth and first order Dirichlet boundary data, corresponding to the "hinged" and the "clamped" cases. By employing the method of L-p approximations, we establish the existence of a special L-infinity minimizer, which solves a divergence PDE system with measure coefficients as parameters. This is a counterpart of the Aronsson-Euler system corresponding to this constrained variational problem. Furthermore, we establish upper and lower bounds for the eigenvalue.