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Divergence-measure fields; i.e., vector fields in L^p and vector-valued Radon measures whose divergences are Radon measures, arise in the study of nonlinear conservation laws and related partial differential equations of divergence form. In this talk we discuss our results on divergence-measure fields in L^(infinity) over sets of finite perimeter, including existence of normal traces and the corresponding Gauss-Green formula. We also present applications of this theory to continuum mechanics and to the initial-boundary value problem of nonlinear hyperbolic conservation laws over sets of finite perimeter.