Sobolev homeomorphism that cannot be approximated by diffeomorphisms in W^{1,1}

  • Stanislav Hencl (University of Prague)
G3 10 (Lecture hall)


We show that it is possible to construct a homeomorphism f in the Sobolev space W^{1,1}([0,1]^4,R^4) such that there are no smooth (or piecewise affine) homeomorphisms f_k that converge to f in W^{1,1} norm. This is joint result with Benjamin Vejnar.

Katja Heid

Bernd Kirchheim

Universität Leipzig

Stephan Luckhaus

Universität Leipzig

Emanuele Spadaro

Max-Planck-Institut für Mathematik in den Naturwissenschaften