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Keywords:
Green’s theorem; elliptic problems; variational problems
Green’s theorem; elliptic problems; variational problems
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 $W^{1,p}()\equiv H^{1,p}()$ $(1\le p<)$.
References:
[1] G.M. Fichtengolc: Differential and Integral Calculus I. Gostechizdat, Moscow, 1951. (Russian)
[2] G.M. Fichtenholz: Differential- und Integralrechnung I. VEB Deutscher Verlag der Wissenschaften, Berlin, 1968. MR 0238635
[3] M. Křížek: An equilibrium finite element method in three-dimensional elasticity. Apl. Mat. 27 (1982), 46–75. MR 0640139
[4] A. Kufner, O. John, S. Fučík: Function Spaces. Academia, Prague, 1977. MR 0482102
[5] J. Nečas: Les Méthodes Directes en Théorie des Equations Elliptiques. Academia, Prague, 1967. MR 0227584
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