Divergence-measure fields, sets of finite perimeter, and conservation laws
The authors analyze divergence-measure fields in \(L^\infty\) over sets of finite perimeter. They introduce the notion of normal traces over boundaries and establish the Gauss-Green formula. The notion of normal traces is shown to be consistent with the notion introduced by \textit{G.-Q. Chen} and \textit{H. Frid} [Arch. Ration. Mech. Anal. 147, No. 2, 89--118 (1999; Zbl 0942.35111)]. In the last section the theory is applied to the initial-boundary-value problem for hyperbolic conservation laws.
scientific article; zbMATH DE number 2155992
scientific article