Surface integral and Gauss--Ostrogradskij theorem from the viewpoint of applications. (Q1775163)

The author gives a detailed proof of the Gauss-Ostrogradskij theorem, which is wrongly presented in some books. A new definition of a domain with a piecewise smooth boundary in \(\mathbb R^3\) is employed and the trace theorem is proved. The surface integral is defined without the partition of unity. Various extensions of the Gauss-Ostrogradskij theorem are considered as well. The paper is a generalization of the author's previous paper [Appl. Math., Praha 44, 55--80 (1999; Zbl 1060.35504)], which is devoted to the line integral.