Green's theorem from the viewpoint of applications. (Q1775158)

The paper contains a new detailed proof of Green's theorem for functions from the Sobolev space \(W^{1,p}\), \(1\leq p < \infty \), defined on bounded two-dimensional domains with a Lipschitz continuous boundary. A special attention is paid to internal an external cusp-points. Line integrals are defined in a natural way without any use of partition of the unity. Divergence forms of Green's theorem are proved in detail as well.