Preprint 1996-040

Lower Semicontinuity of Weighted Path Length in BV

Paolo Baiti and Alberto Bressan

Abstract: 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.

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Lower Semicontinuity of Weighted Path Length in BV
Paolo Baiti, <>
Alberto Bressan, <>
Publishing information:
Accepted for publication in the book ``Geometrical optics and related topics'' of the series ``Progress in nonlinear differential equations and their applications''.
Submitted by:
<> November 28 1996.

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Last modified: Thu Nov 28 17:46:50 1996