| Title:
|
The $L^p$-Helmholtz projection in finite cylinders (English) |
| Author:
|
Nau, Tobias |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
119-134 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article we prove for $1<p<\infty $ the existence of the $L^p$-Helmholtz projection in finite cylinders $\Omega $. More precisely, $\Omega $ is considered to be given as the Cartesian product of a cube and a bounded domain $V$ having $C^1$-boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in $\Omega $ is solved, which implies existence and a representation of the $L^p$-Helmholtz projection as a Fourier multiplier operator. (English) |
| Keyword:
|
Helmholtz projection |
| Keyword:
|
Helmholtz decomposition |
| Keyword:
|
weak Neumann problem |
| Keyword:
|
periodic boundary conditions |
| Keyword:
|
finite cylinder |
| Keyword:
|
cylindrical space domain |
| Keyword:
|
$L^p$-space |
| Keyword:
|
operator-valued Fourier multiplier |
| Keyword:
|
$\mathcal R$-boundedness |
| Keyword:
|
reflection technique |
| Keyword:
|
fluid dynamics |
| MSC:
|
35J20 |
| MSC:
|
35J25 |
| MSC:
|
35Q30 |
| MSC:
|
42B15 |
| MSC:
|
46E40 |
| idZBL:
|
Zbl 06433724 |
| idMR:
|
MR3336028 |
| DOI:
|
10.1007/s10587-015-0163-8 |
| . |
| Date available:
|
2015-04-01T12:25:50Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144216 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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