اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSmooth homeomorphic approximation of piecewise affine homeomorphisms
102
0
0.0
(
0
)
اسأل ChatGPT حول البحث
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 $|f-tilde{f}|_{W^{1,p}(Omega,rn)} < epsilon$.
قيم البحث
اقرأ أيضاً
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
de $Omega$. Using our recently developed scattering control method, we prove that piecewise smooth wave speeds are uniquely determined by this map, and provide a reconstruction formula. In other words, the wave imaging problem is solvable in the piecewise smooth setting under mild conditions. We also illustrate a separate method, likewise constructive, for recovering the locations of interfaces in broken geodesic normal coordinates using scattering control.
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
a new partial data result for Calderon inverse conductivity problem. It is also shown that bisweep data are (up to a constant scaling factor) the Schwartz kernel of the relative Neumann-to-Dirichlet map. A numerical method for reconstructing the supports of inclusions from discrete bisweep data is also presented.
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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
