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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:
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


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