Approximation of W-1,W-p Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian

作者：Campbell Daniel; Hencl Stanislav^*; Tengvall Ville

来源：Advances in Mathematics, 2018, 331: 748-829.

DOI：10.1016/j.aim.2018.04.017

• Jacobian
• Approximation
• Sobolev homeomorphism

Let Omega subset of R-n, n >= 4, be a domain and 1 <= p < [n/2], where [a] stands for the integer part of a. We construct a homeomorphism f is an element of W-1,W-P((-1, 1)(n),R-n) such that J(f) = det D f > 0 on a set of positive measure and J(f) < 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) f(k) such that f(k )-> f in W-1,W-p.

• 出版日期2018-6-20