{"paper":{"title":"Approximation up to the boundary of homeomorphisms of finite Dirichlet energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jani Onninen, Leonid V. Kovalev, Tadeusz Iwaniec","submitted_at":"2011-07-31T19:35:00Z","abstract_excerpt":"Let X and Y be planar Jordan domains of the same finite connectivity, Y being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h:X->Y in the Sobolev space $W^{1,2}$ extends to a continuous map between closed domains. We prove that there exist homeomorphisms between closed domains which converge to h uniformly and in $W^{1,2}$. The problem of approximation of Sobolev homeomorphisms, raised by J. M. Ball and L. C. Evans, is deeply rooted in a study of energy-minimal deformations in nonlinear elasticity. The new feature of our main result is that approximation takes place "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0199","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"}