| Title:
|
Surface integral and Gauss-Ostrogradskij 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:
|
3 |
| Year:
|
1999 |
| Pages:
|
169-241 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Making use of a surface integral defined without use of the partition of unity, trace theorems and the Gauss-Ostrogradskij theorem are proved in the case of three-dimensional domains $\Omega$ with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces $H^{1,p}()$ $(1\le p<)$. The paper is a generalization of the previous author’s paper which is devoted to the line integral. (English) |
| Keyword:
|
variational problems |
| Keyword:
|
surface integral |
| Keyword:
|
trace theorems |
| Keyword:
|
Gauss-Ostrogradskij theorem |
| MSC:
|
35J20 |
| MSC:
|
46E35 |
| MSC:
|
65N99 |
| idZBL:
|
Zbl 1060.46511 |
| idMR:
|
MR1688569 |
| DOI:
|
10.1023/A:1023097018446 |
| . |
| Date available:
|
2009-09-22T18:00:31Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134410 |
| . |
| Reference:
|
[Fi1] G.M. Fichtengolc: Differential and Integral Calculus I.Gostechizdat, Moscow, 1951. (Russian) |
| Reference:
|
[Fi1g] G.M.Fichtenholz: Differential- und Integralrechnung I.VEB Deutscher Verlag der Wissenschaften, Berlin, 1968. Zbl 0164.06002, MR 0238635 |
| Reference:
|
[Fi3] G.M. Fichtengolc: Differential and Integral Calculus III.Gostechizdat, Moscow, 1960. (Russian) |
| Reference:
|
[Fi3g] G.M.Fichtenholz: Differential- und Integralrechnung III.VEB Deutscher Verlag der Wissenschaften, Berlin, 1968. Zbl 0167.32501 |
| Reference:
|
[Kř] M. Křížek: An equilibrium finite element method in three-dimensional elasticity.Apl.Mat. 27 (1982), 46–75. MR 0640139 |
| Reference:
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[KJF] A. Kufner, O. John, S. Fučík: Function Spaces.Academia, Prague, 1977. MR 0482102 |
| Reference:
|
[Ne] J. Nečas: Les Méthodes Directes en Théorie des Equations Elliptiques.Academia, Prague, 1967. MR 0227584 |
| Reference:
|
[NH] J. Nečas, I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier, Amsterdam, 1981. MR 0600655 |
| Reference:
|
[PF] Zs. Pach, T. Frey: Vector- and Tensoranalysis.Müszaki könyvkiadó, Budapest, 1960. (Hungarian) |
| Reference:
|
[Sa] S. Saks: Theory of the Integral.Hafner Publ. Comp., New York, 1937. Zbl 0017.30004, MR 0167578 |
| Reference:
|
[Si] R. Sikorski: Differential and Integral Calculus (Functions of more variables).Państwowe wydawnictwo naukowe, Warsaw, 1969. (Polish) MR 0592423 |
| Reference:
|
[ŠT] J. Škrášek, Z. Tichý: Foundations of Applied Mathematics II.SNTL, Prague, 1986. (Czech) |
| Reference:
|
[Že] A. Ženíšek: Green’s theorem from the viewpoint of applications.Appl. Math. 44 (1999), 55–80. MR 1666842, 10.1023/A:1022272204023 |
| . |
