| Title:
|
The Neumann problem for the Laplace equation on general domains (English) |
| Author:
|
Medková, Dagmar |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
1107-1139 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Laplace equation |
| Keyword:
|
Neumann problem |
| Keyword:
|
potential |
| Keyword:
|
boundary integral equation method |
| MSC:
|
31B10 |
| MSC:
|
35D05 |
| MSC:
|
35J05 |
| MSC:
|
35J25 |
| idZBL:
|
Zbl 1174.31305 |
| idMR:
|
MR2357583 |
| . |
| Date available:
|
2009-09-24T11:52:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128230 |
| . |
| Reference:
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