Counterexamples in calculus of variations in L∞ through the vectorial Eikonal equationKatzourakis, N. and Shaw, G. (2018) Counterexamples in calculus of variations in L∞ through the vectorial Eikonal equation. Comptes Rendus Mathematique, 356 (5). pp. 498-502. ISSN 1631-073X
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1016/j.crma.2018.04.010 Abstract/SummaryWe 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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