Approximation up to the boundary of homeomorphisms of finite Dirichlet energy

作者：Iwaniec Tadeusz^*; Kovalev Leonid V; Onninen Jani

来源：Bulletin of the London Mathematical Society, 2012, 44: 871-881.

DOI：10.1112/blms/bds016

Let X subset of C and Y subset of C be Jordan domains of the same finite connectivity, Y being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h: X -%26gt; Y in the Sobolev space W-1,W-2 extends to a continuous map h: (X)over-bar -%26gt; (Y)over-bar. We prove that there exist homeomorphisms h(k): (X)over-bar -%26gt; (Y)over-bar that converge to h uniformly and in W-1,W-2(X, Y). 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.

• 出版日期2012-10