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variational problems; surface integral; trace theorems; Gauss-Ostrogradskij theorem
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.
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