Abstract
We analyze a class of L 1 vector elds, called divergence-measure elds. We establish the Gauss-Green formula, the normal traces over subsets of Lipschitz boundaries, and the product rule for this class of L 1 elds. Then we apply this theory to analyzeL 1 entropy solutions of initial-boundary-value problems for hyperbolic conservation laws and to study the ways in which the solutions assume their initial and boundary data. The examples of conservation laws include multidimensional scalar equations, the system of nonlinear elasticity, and a class ofm m systems with afne characteristic hypersurfaces. The analysis inL 1 also extends toL p .
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