Abstract
We show that, for any regular bounded domain Ω⊆Rn, n=2,3, there exist infinitely many global diffeomorphisms equal to the identity on ∂Ω that solve the Eikonal equation. We also provide explicit examples of such maps on annular domains. This implies that the ∞-Laplace system arising in vectorial calculus of variations in L∞ does not suffice to characterise either limits of p-Harmonic maps as p→∞ or absolute minimisers in the sense of Aronsson.
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