Explicit Singular Viscosity Solutions of the Aronsson Equation
Abstract
We establish that when n >= 2 and H is a C1 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-C1 and nowhere twice differentiable. In particular, we supplement the C1 regularity result of Wang and Yu by deducing that strict level convexity is necessary for C1 regularity of solutions.
0