Geodesic
Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications
Applications of Mathematics, Tome 44 (1999) no. 3, pp. 169-241 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Making use of a surface integral defined without use of the partition of unity, trace theorems and the Gauss-Ostrogradskij theorem are proved in the case of three-dimensional domains $\Omega$ with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces $H^{1,p}()$ $(1\le p)$. The paper is a generalization of the previous author’s paper which is devoted to the line integral.
Making use of a surface integral defined without use of the partition of unity, trace theorems and the Gauss-Ostrogradskij theorem are proved in the case of three-dimensional domains $\Omega$ with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces $H^{1,p}()$ $(1\le p)$. The paper is a generalization of the previous author’s paper which is devoted to the line integral.
DOI : 10.1023/A:1023097018446
Classification : 35J20, 46E35, 65N99
Keywords: variational problems; surface integral; trace theorems; Gauss-Ostrogradskij theorem 
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     title = {Surface integral and {Gauss-Ostrogradskij} theorem from the viewpoint of applications},
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     year = {1999},
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Ženíšek, Alexander. Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications. Applications of Mathematics, Tome 44 (1999) no. 3, pp. 169-241. doi: 10.1023/A:1023097018446

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