A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces

Katrin Schumacher

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 3, page 637-648
  • ISSN: 0011-4642

Abstract

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Given a domain Ω of class C k , 1 , k , we construct a chart that maps normals to the boundary of the half space to normals to the boundary of Ω in the sense that ( - x n ) α ( x ' , 0 ) = - N ( x ' ) and that still is of class C k , 1 . As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to k on domains of class C k , 1 . The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.

How to cite

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Schumacher, Katrin. "A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces." Czechoslovak Mathematical Journal 59.3 (2009): 637-648. <http://eudml.org/doc/37948>.

@article{Schumacher2009,
abstract = {Given a domain $\Omega $ of class $C^\{k,1\}$, $k\in \mathbb \{N\} $, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of $\Omega $ in the sense that $(\partial - \{\partial x_n\})\alpha (x^\{\prime \},0)= - N(x^\{\prime \})$ and that still is of class $C^\{k,1\}$. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to $k$ on domains of class $C^\{k,1\}$. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.},
author = {Schumacher, Katrin},
journal = {Czechoslovak Mathematical Journal},
keywords = {chart; coordinate transformation; normal vector; normal derivative; extension theorem; Muckenhoupt weight; chart; coordinate transformation; normal vector; normal derivative; extension theorem; Muckenhoupt weight},
language = {eng},
number = {3},
pages = {637-648},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces},
url = {http://eudml.org/doc/37948},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Schumacher, Katrin
TI - A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 637
EP - 648
AB - Given a domain $\Omega $ of class $C^{k,1}$, $k\in \mathbb {N} $, we construct a chart that maps normals to the boundary of the half space to normals to the boundary of $\Omega $ in the sense that $(\partial - {\partial x_n})\alpha (x^{\prime },0)= - N(x^{\prime })$ and that still is of class $C^{k,1}$. As an application we prove the existence of a continuous extension operator for all normal derivatives of order 0 to $k$ on domains of class $C^{k,1}$. The construction of this operator is performed in weighted function spaces where the weight function is taken from the class of Muckenhoupt weights.
LA - eng
KW - chart; coordinate transformation; normal vector; normal derivative; extension theorem; Muckenhoupt weight; chart; coordinate transformation; normal vector; normal derivative; extension theorem; Muckenhoupt weight
UR - http://eudml.org/doc/37948
ER -

References

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