Diffeomorphic approximation of Planar Sobolev Homeomorphisms in rearrangement invariant spaces

Let $Ω\subseteq\mathcal{R}^2$ be a domain, let $X$ be a rearrangement invariant space and let $f\in W^{1}X(Ω,\mathcal{R}^2)$ be a homeomorphism between $Ω$ and $f(Ω)$. Then there exists a sequence of diffeomorphisms $f_k$ converging to $f$ in the space $W^{1}X(Ω,\mathcal{R}^2)$.

No reviews yet.

No comments yet.