Geodesic
Green's theorem from the viewpoint of applications
Applications of Mathematics, Tome 44 (1999) no. 1, pp. 55-80

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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 $W^{1,p}()\equiv H^{1,p}()$ $(1\le p)$.
DOI : 10.1023/A:1022272204023
Classification : 26B20, 35J05, 35J20, 65N99
Keywords: Green’s theorem; elliptic problems; variational problems 
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Ženíšek, Alexander. Green's theorem from the viewpoint of applications. Applications of Mathematics, Tome 44 (1999) no. 1, pp. 55-80. doi: 10.1023/A:1022272204023

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