Lower semicontinuity of weighted path length in BV
We establish some basic lower semicontinuity properties for a class of weighted metrics in BV. These Riemann-type metrics, uniformly equivalent to the L 1 distance, are defined in terms of the Glimm interaction potential. They are relevant in the study of nonlinear hyperbolic systems of conservation laws, being contractive w.r.t. the corresponding flow of solutions.
KeywordsRiemann Problem Weighted Distance Finsler Manifold Interaction Estimate Elementary Path
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