| Title:
|
A chart preserving the normal vector and extensions of normal derivatives in weighted function spaces (English) |
| Author:
|
Schumacher, Katrin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
637-648 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given a domain $\Omega $ of class $C^{k,1}$, $k\in \Bbb 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 $(\partial- {\partial x_n})\alpha (x',0)= - N(x')$ 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. (English) |
| Keyword:
|
chart |
| Keyword:
|
coordinate transformation |
| Keyword:
|
normal vector |
| Keyword:
|
normal derivative |
| Keyword:
|
extension theorem |
| Keyword:
|
Muckenhoupt weight |
| MSC:
|
35A25 |
| MSC:
|
35A99 |
| MSC:
|
46E35 |
| MSC:
|
46N20 |
| MSC:
|
47A20 |
| idZBL:
|
Zbl 1218.47019 |
| idMR:
|
MR2545646 |
| . |
| Date available:
|
2010-07-20T15:31:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140506 |
| . |
| Reference:
|
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| . |
