The weak and strong closures of Sobolev homeomorphisms are the same
Complex Variables
2012-01-19 v1
Abstract
Let X and Y be bounded multiply connected Lipschitz domains in \R^2. We consider the class H_p (X, Y) of homeomorphisms h : X -> Y in the Sobolev space W^{1,p} (X, \R^2). We prove that the weak and strong closures of H_p (X, Y), 2 \le p< \infty, are equal. The importance of this result to the existence theory in the calculus of variations and anticipated applications to nonlinear elasticity are captured by Theorem 1.5.
Keywords
Cite
@article{arxiv.1201.3864,
title = {The weak and strong closures of Sobolev homeomorphisms are the same},
author = {Tadeusz Iwaniec and Jani Onninen},
journal= {arXiv preprint arXiv:1201.3864},
year = {2012}
}
Comments
30 pages, 1 figure