ﻻ يوجد ملخص باللغة العربية
Let $Omegasubseteqmathcal{R}^2$ be a domain, let $X$ be a rearrangement invariant space and let $fin W^{1}X(Omega,mathcal{R}^2)$ be a homeomorphism between $Omega$ and $f(Omega)$. Then there exists a sequence of diffeomorphisms $f_k$ converging to $f$ in the space $W^{1}X(Omega,mathcal{R}^2)$.
Given a Sobolev homeomorphism $fin W^{2,1}$ in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of $epsilon$ measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms in the $W^{2,1}$ norm on this set.
Let $Omega$ be an internal chord-arc Jordan domain and $varphi:mathbb SrightarrowpartialOmega$ be a homeomorphism. We show that $varphi$ has finite dyadic energy if and only if $varphi$ has a diffeomorphic extension $h: mathbb Drightarrow Omega$ which has finite energy.
We present a classification of strict limits of planar BV homeomorphisms. The authors and S. Hencl showed in a previous work cite{CHKR} that such mappings allow for cavitations and fractures singularities but fulfill a suitable generalization of the
Given any $f$ a locally finitely piecewise affine homeomorphism of $Omega subset rn$ onto $Delta subset rn$ in $W^{1,p}$, $1leq p < infty$ and any $epsilon >0$ we construct a smooth injective map $tilde{f}$ such that $|f-tilde{f}|_{W^{1,p}(Omega,rn)} < epsilon$.
Let $Omega subset mathbb{R}^n$ be an open set and $f_k in W^{s,p}(Omega;mathbb{R}^n)$ be a sequence of homeomorphisms weakly converging to $f in W^{s,p}(Omega;mathbb{R}^n)$. It is known that if $s=1$ and $p > n-1$ then $f$ is injective almost everywh