×
Ženíšek, Alexander

Surface integral and Gauss–Ostrogradskij theorem from the viewpoint of applications. (English) Zbl 1060.46511

Appl. Math., Praha 44, No. 3, 169-241 (1999).
The author gives a detailed proof of the Gauss-Ostrogradskij theorem, which is wrongly presented in some books. A new definition of a domain with a piecewise smooth boundary in \(\mathbb R^3\) is employed and the trace theorem is proved. The surface integral is defined without the partition of unity. Various extensions of the Gauss-Ostrogradskij theorem are considered as well. The paper is a generalization of the author’s previous paper [Appl. Math., Praha 44, 55–80 (1999; Zbl 1060.35504)], which is devoted to the line integral.
Reviewer: Michal Křížek (Praha)

Cited in 1 Document

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35J20 Variational methods for second-order elliptic equations
65N99 Numerical methods for partial differential equations, boundary value problems

Keywords:

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

Citations:

Zbl 1060.35504
PDF BibTeX XML Cite
\textit{A. Ženíšek}, Appl. Math., Praha 44, No. 3, 169--241 (1999; Zbl 1060.46511)
Full Text: DOI EuDML
  • logo of hbz
  • logo of WorldCat

References:

[1] G.M. Fichtengolc: Differential and Integral Calculus I. Gostechizdat, Moscow, 1951.
[2] G.M.Fichtenholz: Differential- und Integralrechnung I. VEB Deutscher Verlag der Wissenschaften, Berlin, 1968. · Zbl 0164.06002
[3] G.M. Fichtengolc: Differential and Integral Calculus III. Gostechizdat, Moscow, 1960.
[4] G.M.Fichtenholz: Differential- und Integralrechnung III. VEB Deutscher Verlag der Wissenschaften, Berlin, 1968. · Zbl 0167.32501
[5] M. Křížek: An equilibrium finite element method in three-dimensional elasticity. Apl.Mat. 27 (1982), 46-75.
[6] A. Kufner, O. John, S. Fučík: Function Spaces. Academia, Prague, 1977.
[7] J. Nečas: Les Méthodes Directes en Théorie des Equations Elliptiques. Academia, Prague, 1967. · Zbl 1225.35003
[8] J. Nečas, I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier, Amsterdam, 1981.
[9] Zs. Pach, T. Frey: Vector- and Tensoranalysis. Müszaki könyvkiadó, Budapest, 1960.
[10] S. Saks: Theory of the Integral. Hafner Publ. Comp., New York, 1937. · Zbl 0017.30004
[11] R. Sikorski: Differential and Integral Calculus (Functions of more variables). Państwowe wydawnictwo naukowe, Warsaw, 1969. · Zbl 0182.37901
[12] J. Škrášek, Z. Tichý: Foundations of Applied Mathematics II. SNTL, Prague, 1986.
[13] A. Ženíšek: Green’s theorem from the viewpoint of applications. Appl. Math. 44 (1999), 55-80. · Zbl 1060.35504
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.