Green's theorem from the viewpoint of applications

Abstract:

Making use of a line integral defined without use of the partition of unity, Green's theorem is proved in the case of two-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces W^{1, p} (\Omega) \equiv H^{1,p} (\Omega) (1 p < ).

Keywords: Green's theorem; elliptic problems; variational problems

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