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Lower semicontinuity of weighted path length in BV. (English) Zbl 0891.35089
Colombini, Ferruccio (ed.) et al., Geometrical optics and related topics. Selected papers of the meeting, Cortona, Italy, September 1996. Boston, MA: Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 32, 31-58 (1997).
Summary: 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 with respect to the corresponding flow of solutions.
For the entire collection see [Zbl 0878.00061].

##### MSC:
 35L65 Hyperbolic conservation laws 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 58C07 Continuity properties of mappings on manifolds
##### Keywords:
Glimm interaction potential