| Title:
|
Essential norms of a potential theoretic boundary integral operator in $L\sp 1$ (English) |
| Author:
|
Král, Josef |
| Author:
|
Medková, Dagmar |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
123 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
419-436 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G \subset\Bbb R^m$ $(m \ge2)$ be an open set with a compact boundary $B$ and let $\sigma\ge0$ be a finite measure on $B$. Consider the space $L^1(\sigma)$ of all $\sigma$-integrable functions on $B$ and, for each $f \in L^1(\sigma)$, denote by $f \sigma$ the signed measure on $B$ arising by multiplying $\sigma$ by $f$ in the usual way. $\Cal N_{\sigma}f$ denotes the weak normal derivative (w.r. to $G$) of the Newtonian (in case $m >2$) or the logarithmic (in case $n=2$) potential of $f\sigma$, correspondingly. Sharp geometric estimates are obtained for the essential norms of the operator $\Cal N_{\sigma} - \alpha I$ (here $\alpha\in\Bbb R$ and $I$ stands for the identity operator on $L^1(\sigma)$) corresponding to various norms on $L^1(\sigma)$ inducing the topology of standard convergence in the mean w.r. to $\sigma$. (English) |
| Keyword:
|
single layer potential |
| Keyword:
|
weak normal derivative |
| Keyword:
|
essential norm |
| MSC:
|
31A10 |
| MSC:
|
31B10 |
| MSC:
|
31B20 |
| MSC:
|
31B25 |
| idZBL:
|
Zbl 0936.31007 |
| idMR:
|
MR1667114 |
| DOI:
|
10.21136/MB.1998.125966 |
| . |
| Date available:
|
2009-09-24T21:33:55Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125966 |
| . |
| 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:
|
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| . |
