# Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications

Applications of Mathematics (1999)

- Volume: 44, Issue: 3, page 169-241
- ISSN: 0862-7940

## Access Full Article

top## Abstract

top## How to cite

topŽeníšek, Alexander. "Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications." Applications of Mathematics 44.3 (1999): 169-241. <http://eudml.org/doc/33031>.

@article{Ženíšek1999,

abstract = {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.},

author = {Ženíšek, Alexander},

journal = {Applications of Mathematics},

keywords = {variational problems; surface integral; trace theorems; Gauss-Ostrogradskij theorem; variational problems; surface integral; trace theorems; Gauss–Ostrogradskij theorem},

language = {eng},

number = {3},

pages = {169-241},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications},

url = {http://eudml.org/doc/33031},

volume = {44},

year = {1999},

}

TY - JOUR

AU - Ženíšek, Alexander

TI - Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications

JO - Applications of Mathematics

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 44

IS - 3

SP - 169

EP - 241

AB - 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.

LA - eng

KW - variational problems; surface integral; trace theorems; Gauss-Ostrogradskij theorem; variational problems; surface integral; trace theorems; Gauss–Ostrogradskij theorem

UR - http://eudml.org/doc/33031

ER -

## References

top- Differential and Integral Calculus I, Gostechizdat, Moscow, 1951. (Russian) (1951)
- Differential- und Integralrechnung I, VEB Deutscher Verlag der Wissenschaften, Berlin, 1968. (1968) Zbl0164.06002MR0238635
- Differential and Integral Calculus III, Gostechizdat, Moscow, 1960. (Russian) (1960)
- Differential- und Integralrechnung III, VEB Deutscher Verlag der Wissenschaften, Berlin, 1968. (1968) Zbl0167.32501
- An equilibrium finite element method in three-dimensional elasticity, Apl.Mat. 27 (1982), 46–75. (1982) MR0640139
- Function Spaces, Academia, Prague, 1977. (1977) MR0482102
- Les Méthodes Directes en Théorie des Equations Elliptiques, Academia, Prague, 1967. (1967) MR0227584
- Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier, Amsterdam, 1981. (1981) MR0600655
- Vector- and Tensoranalysis, Müszaki könyvkiadó, Budapest, 1960. (Hungarian) (1960)
- Theory of the Integral, Hafner Publ. Comp., New York, 1937. (1937) Zbl0017.30004MR0167578
- Differential and Integral Calculus (Functions of more variables), Państwowe wydawnictwo naukowe, Warsaw, 1969. (Polish) (1969) MR0592423
- Foundations of Applied Mathematics II, SNTL, Prague, 1986. (Czech) (1986)
- 10.1023/A:1022272204023, Appl. Math. 44 (1999), 55–80. (1999) MR1666842DOI10.1023/A:1022272204023

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.