Preprint 1996-040

Lower Semicontinuity of Weighted Path Length in BV

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.

Paper:

Available as PostScript

Title:

Lower Semicontinuity of Weighted Path Length in BV

Author(s):

Paolo Baiti, mailto:baiti@sissa.it

Alberto Bressan, mailto:bressan@sissa.it

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:

mailto:baiti@sissa.it November 28 1996.