ﻻ يوجد ملخص باللغة العربية
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 $|f-tilde{f}|_{W^{1,p}(Omega,rn)} < epsilon$.
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 $c$ be a piecewise smooth wave speed on $mathbb R^n$, unknown inside a domain $Omega$. We are given the solution operator for the scalar wave equation $(partial_t^2-c^2Delta)u=0$, but only outside $Omega$ and only for initial data supported outsi
Conductivity equation is studied in piecewise smooth plane domains and with measure-valued current patterns (Neumann boundary values). This allows one to extend the recently introduced concept of bisweep data to piecewise smooth domains, which yields
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 $W^{1}X(Omega,mathcal{R}^2)$.
We show that certain groups of piecewise linear homeomorphims of the interval are invariably generated.