Solution of the Neumann problem for the Laplace equation

Dagmar Medková

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 4, page 763-784
  • ISSN: 0011-4642

Abstract

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For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.

How to cite

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Medková, Dagmar. "Solution of the Neumann problem for the Laplace equation." Czechoslovak Mathematical Journal 48.4 (1998): 763-784. <http://eudml.org/doc/30453>.

@article{Medková1998,
abstract = {For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.},
author = {Medková, Dagmar},
journal = {Czechoslovak Mathematical Journal},
keywords = {single layer potential; generalized normal derivative; single layer potential; generalized normal derivative; double layer potential},
language = {eng},
number = {4},
pages = {763-784},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solution of the Neumann problem for the Laplace equation},
url = {http://eudml.org/doc/30453},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Medková, Dagmar
TI - Solution of the Neumann problem for the Laplace equation
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 4
SP - 763
EP - 784
AB - For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.
LA - eng
KW - single layer potential; generalized normal derivative; single layer potential; generalized normal derivative; double layer potential
UR - http://eudml.org/doc/30453
ER -

References

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Citations in EuDML Documents

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  1. Dagmar Medková, The Neumann problem for the Laplace equation on general domains
  2. Dagmar Medková, The boundary-value problems for Laplace equation and domains with nonsmooth boundary
  3. Dagmar Medková, Continuous extendibility of solutions of the Neumann problem for the Laplace equation
  4. Dagmar Medková, Continuous extendibility of solutions of the third problem for the Laplace equation
  5. Dagmar Medková, Boundedness of the solution of the third problem for the Laplace equation
  6. Dagmar Medková, Solution of the Dirichlet problem for the Laplace equation

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