  We establish that when n >= 2 and H is a C^1 Hamiltonian such that some level
set contains a line segment, the Aronsson equation admits explicit entire
viscosity solutions. They are superpositions of a linear part plus a Lipschitz
continuous everywhere differentiable singular part which in general is non-C^1
and nowhere twice differentiable. In particular, we supplement the C^1
regularity result of Wang and Yu by deducing that strict level convexity is
necessary for C^1 regularity of solutions.
