2018/01/29 by Katzourakis, Nikos, Shaw, Giles
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1801.09756
We show that for any regular bounded domain Ω⊆ \mathbb Rn, n=2,3, there exist infinitely many global diffeomorphisms equal to the identity on ∂ Ω which 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.