Surface integral and Gauss–Ostrogradskij theorem from the viewpoint of applications. (English) Zbl 1060.46511

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.


46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35J20 Variational methods for second-order elliptic equations
65N99 Numerical methods for partial differential equations, boundary value problems


Zbl 1060.35504
Full Text: DOI EuDML


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