Admissible solutions of nonlinear systems of conservation laws in arbitrary dimensions are identified as points in the range of boundedly Frechet differentiable map of boundary data into weak solutions. For Cauchy problems for scalar conservation laws or hyperbolic systems in one space dimension, admissibility so determined agrees fairly closely with familiar entropy conditions.
For systems in higher dimensions, however, the set of admissible weak solutions is materially smaller than might be anticipated, computational evidence to the contrary notwithstanding. Such is provably the case for Cauchy problems for hyperbolic systems, and is strongly suggested by results obtained for reduced systems determining stationary or self-similar solutions.