Abstract
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 Ω with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces H 1,p(Ω) (1 ≤ p < ∞). The paper is a generalization of the previous author's paper which is devoted to the line integral.
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Ženíšek, A. Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications. Applications of Mathematics 44, 169–241 (1999). https://doi.org/10.1023/A:1023097018446
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DOI: https://doi.org/10.1023/A:1023097018446