| Title:
|
Some examples concerning applicability of the Fredholm-Radon method in potential theory (English) |
| Author:
|
Král, Josef |
| Author:
|
Wendland, Wolfgang |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1986 |
| Pages:
|
293-308 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Simple examples of bounded domains $D\subset \bold R^3$ are considered for which the presence of peculiar corners and edges in the boundary $\delta D$ causes that the double layer potential operator acting on the space $\Cal S(\delta D)$ of all continuous functions on $\delta D$ can for no value of the parameter $\alpha$ be approximated (in the sub-norm) by means of operators of the form $\alpha I+T$ (where $I$ is the identity operator and $T$ is a compact linear operator) with a deviation less then $|\alpha|$; on the other hand, such approximability turns out to be possible for $\alpha = \frac 12$ if a new norm is introduced in $\Cal S(\delta D)$ with help of a suitable weight function. (English) |
| Keyword:
|
double layer potential |
| Keyword:
|
Fredholm-Radom method in potential theory |
| Keyword:
|
rectangular |
| Keyword:
|
compact boundary |
| Keyword:
|
Dirichlet problem |
| Keyword:
|
Neumann problem |
| MSC:
|
31B20 |
| MSC:
|
47A53 |
| MSC:
|
47B38 |
| idZBL:
|
Zbl 0615.31005 |
| idMR:
|
MR0854323 |
| DOI:
|
10.21136/AM.1986.104208 |
| . |
| Date available:
|
2008-05-20T18:30:24Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104208 |
| . |
| 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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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[11] J. Radon: Über die Randwertaufgaben beim logarithmischen Potential.ibid. 1123-1167. Zbl 0061.23403 |
| Reference:
|
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| Reference:
|
[13] G. Verchota: Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains.J. of Functional Analysis 59 (1984), 572-611. Zbl 0589.31005, MR 0769382, 10.1016/0022-1236(84)90066-1 |
| Reference:
|
[14] W. Wendland: Lösung der ersten und zweiten Randwertaufgaben des Innen- und Aussengebietes für Potentialgleichung im $R_3$ durch Randbelegungen.Bericht des Hahn-Meitner Institute für Kernforschung Berlin, HMI-B 41, BM 19 (1965), 1-99. MR 0232010 |
| Reference:
|
[15] W. Wendland: Die Behandlung von Randwertaufgaben im $R^3$ mit Hilfe von Einfach und Doppelschichtpotentialen.Numerische Mathematik 11 (1968), 380-404. MR 0231550, 10.1007/BF02161886 |
| Reference:
|
[16] W. Wendland: Boundary element methods and their asymptotic convergence.Preprint Nr. 690, TH Darmstadt (1982), 1-82. MR 0762829 |
| Reference:
|
[17] T. S. Angell R. E. Kleinman J. Král: Double layer potentials on boundaries with corners and edges.Comment. Math. Univ. Carolinae 27 (1986). |
| . |
