| Title:
|
Green's theorem from the viewpoint of applications (English) |
| Author:
|
Ženíšek, Alexander |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
55-80 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Making use of a line integral defined without use of the partition of unity, Green’s theorem is proved in the case of two-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces $W^{1,p}()\equiv H^{1,p}()$ $(1\le p<)$. (English) |
| Keyword:
|
Green’s theorem |
| Keyword:
|
elliptic problems |
| Keyword:
|
variational problems |
| MSC:
|
26B20 |
| MSC:
|
35J05 |
| MSC:
|
35J20 |
| MSC:
|
65N99 |
| idZBL:
|
Zbl 1060.35504 |
| idMR:
|
MR1666842 |
| DOI:
|
10.1023/A:1022272204023 |
| . |
| Date available:
|
2009-09-22T18:00:03Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134406 |
| . |
| Reference:
|
[1] G.M. Fichtengolc: Differential and Integral Calculus I.Gostechizdat, Moscow, 1951. (Russian) |
| Reference:
|
[2] G.M. Fichtenholz: Differential- und Integralrechnung I.VEB Deutscher Verlag der Wissenschaften, Berlin, 1968. MR 0238635 |
| Reference:
|
[3] M. Křížek: An equilibrium finite element method in three-dimensional elasticity.Apl. Mat. 27 (1982), 46–75. MR 0640139 |
| Reference:
|
[4] A. Kufner, O. John, S. Fučík: Function Spaces.Academia, Prague, 1977. MR 0482102 |
| Reference:
|
[5] J. Nečas: Les Méthodes Directes en Théorie des Equations Elliptiques.Academia, Prague, 1967. MR 0227584 |
| . |
