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Article

Ženíšek, Alexander
Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications. (English). Applications of Mathematics, vol. 44 (1999), issue 3, pp. 169-241
MSC: 35J20, 46E35, 65N99 | MR 1688569 | Zbl 1060.46511 | DOI: 10.1023/A:1023097018446
Keywords:
variational problems; surface integral; trace theorems; Gauss-Ostrogradskij theorem
Summary:
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.
References:
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