Alexander Zenisek, Department of Mathematics, Technical University Brno, Technicka 2, 616 69 Brno, Czech Republic, e-mail: zenisek@mat.fme.vutbr.cz
Abstract: 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 $W^{1,p}(\Om)\equiv H^{1,p}(\Om)$ $(1\le p<\IY)$.
Keywords: Green's theorem, elliptic problems, variational problems
Classification (MSC 1991): 65N99
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