{"paper":{"title":"Super regularity for Beltrami systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaven J. Martin","submitted_at":"2019-03-03T22:47:04Z","abstract_excerpt":"We prove a surprising higher regularity for solutions to the nonlinear elliptic autonomous Beltrami equation in a planar domain $\\Omega$, \\[ f_\\zbar = {\\cal A}(f_z) \\hskip15pt a.e.\\;\\; z\\in \\Omega, \\] when ${\\cal A}$ is linear at $\\infty$. Namely $W^{1,1}_{loc}(\\Omega)$ solutions are $W^{2,2+\\epsilon}_{loc}(\\Omega)$. Here $\\epsilon>0$ depends explicitly on the ellipticity bounds of ${\\cal A}$. The condition ``is linear at $\\infty$'' is necessary - the result is false for the equation $f_\\zbar = k|f_z|$, for any $0<k<1$, ($k=0$ is Weyl's lemma).\n  We discuss the subsequent higher regularity imp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.01008","kind":"arxiv","version":1},"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"}