Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications

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 with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces H^1,p() (1 p < ). The paper is a generalization of the previous author's paper which is devoted to the line integral.

Keywords: variational problems; surface integral; trace theorems; Gauss-Ostrogradskij theorem

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, Technical University Brno, Technická 2, 616 69 Brno, Czech Republic, zenisek@mat.fme.vutbr.cz