2011/08/31 by Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Boundary (topology) #Discrete mathematics #Homeomorphism (graph theory) #Lipschitz continuity #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Nonlinear system #Planar #Pure mathematics #Sobolev space #math.CV #msc:30E10 #msc:46E35 #msc:58E20
paper · pdf · doi:10.1112/blms/bds016
published as Bull. Lond. Math. Soc. 44 (2012), no. 5, 871-881 · Three figures
openalex publication_date 2012/03/20 · arxiv created 2013/02/09 · arxiv updated 2013/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let 핏⊂ℂ and 핐⊂ℂ be Jordan domains of the same finite connectivity, 핐 being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h: 핏→핐 in the Sobolev space 풲1, 2 extends to a continuous map h: 핏→핐. We prove that there exist homeomorphisms hk: 핏→핐 that converge to h uniformly and in 풲1, 2(핏, 핐). 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 non-linear elasticity. The new feature of our main result is that approximation takes place also on the boundary, where the original map need not be a homeomorphism.