{"paper":{"title":"Counterexamples in Calculus of Variations in $L^\\infty$ through the vectorial Eikonal equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giles Shaw, Nikos Katzourakis (Reading, UK)","submitted_at":"2018-01-29T20:57:47Z","abstract_excerpt":"We show that for any regular bounded domain $\\Omega\\subseteq \\mathbb R^n$, $n=2,3$, there exist infinitely many global diffeomorphisms equal to the identity on $\\partial \\Omega$ which solve the Eikonal equation. We also provide explicit examples of such maps on annular domains. This implies that the $\\infty$-Laplace system arising in vectorial Calculus of Variations in $L^\\infty$ does not suffice to characterise either limits of $p$-Harmonic maps as $p\\to \\infty$, or absolute minimisers in the sense of Aronsson."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09756","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}