Explicit Singular Viscosity Solutions of the Aronsson Equation

Abstract

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.

arXiv comment4 pages, 1 figure, new simplified proof

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