The Neumann problem for the Laplace equation on general domains

Dagmar Medková

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 4, page 1107-1139
  • ISSN: 0011-4642

Abstract

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The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set G in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on ∂ G . If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on G a necessary and sufficient condition for the solvability of the problem is given and the solution is constructed.

How to cite

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Medková, Dagmar. "The Neumann problem for the Laplace equation on general domains." Czechoslovak Mathematical Journal 57.4 (2007): 1107-1139. <http://eudml.org/doc/31185>.

@article{Medková2007,
abstract = {The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set $G$ in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on $\partial G$. If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on $G$ a necessary and sufficient condition for the solvability of the problem is given and the solution is constructed.},
author = {Medková, Dagmar},
journal = {Czechoslovak Mathematical Journal},
keywords = {Laplace equation; Neumann problem; potential; boundary integral equation method; Laplace equation; Neumann problem; potential; boundary integral equation method},
language = {eng},
number = {4},
pages = {1107-1139},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Neumann problem for the Laplace equation on general domains},
url = {http://eudml.org/doc/31185},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Medková, Dagmar
TI - The Neumann problem for the Laplace equation on general domains
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 4
SP - 1107
EP - 1139
AB - The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set $G$ in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on $\partial G$. If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on $G$ a necessary and sufficient condition for the solvability of the problem is given and the solution is constructed.
LA - eng
KW - Laplace equation; Neumann problem; potential; boundary integral equation method; Laplace equation; Neumann problem; potential; boundary integral equation method
UR - http://eudml.org/doc/31185
ER -

References

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