Some examples concerning applicability of the Fredholm-Radon method in potential theory

Aplikace matematiky (1986)

• Volume: 31, Issue: 4, page 293-308
• ISSN: 0862-7940

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Abstract

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Simple examples of bounded domains $D\subset {𝐑}^{3}$ 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 $𝒮\left(\delta D\right)$ 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 $\alpha =\frac{1}{2}$ if a new norm is introduced in $𝒮\left(\delta D\right)$ with help of a suitable weight function.

How to cite

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Král, Josef, and Wendland, Wolfgang L.. "Some examples concerning applicability of the Fredholm-Radon method in potential theory." Aplikace matematiky 31.4 (1986): 293-308. <http://eudml.org/doc/15456>.

@article{Král1986,
abstract = {Simple examples of bounded domains $D\subset \mathbf \{R\}^3$ 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 $\mathcal \{S\}(\delta D)$ 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 $\alpha = \frac\{1\}\{2\}$ if a new norm is introduced in $\mathcal \{S\}(\delta D)$ with help of a suitable weight function.},
author = {Král, Josef, Wendland, Wolfgang L.},
journal = {Aplikace matematiky},
keywords = {double layer potential; Fredholm-Radom method in potential theory; rectangular; compact boundary; Dirichlet problem; Neumann problem; rectangular; compact boundary; Fredholm-Radon method; Dirichlet problem; double layer potential; Neumann problem},
language = {eng},
number = {4},
pages = {293-308},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some examples concerning applicability of the Fredholm-Radon method in potential theory},
url = {http://eudml.org/doc/15456},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Král, Josef
AU - Wendland, Wolfgang L.
TI - Some examples concerning applicability of the Fredholm-Radon method in potential theory
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 4
SP - 293
EP - 308
AB - Simple examples of bounded domains $D\subset \mathbf {R}^3$ 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 $\mathcal {S}(\delta D)$ 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 $\alpha = \frac{1}{2}$ if a new norm is introduced in $\mathcal {S}(\delta D)$ with help of a suitable weight function.
LA - eng
KW - double layer potential; Fredholm-Radom method in potential theory; rectangular; compact boundary; Dirichlet problem; Neumann problem; rectangular; compact boundary; Fredholm-Radon method; Dirichlet problem; double layer potential; Neumann problem
UR - http://eudml.org/doc/15456
ER -

References

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