Initial-boundary value problems for continuity equations with BV coefficients
Analysis of PDEs
2013-04-04 v1
Abstract
We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coefficients at the boundary of the domain. We also discuss some examples showing that, regardless the orientation of the coefficients at the boundary, uniqueness may be violated as soon as the BV regularity deteriorates at the boundary.
Cite
@article{arxiv.1304.0975,
title = {Initial-boundary value problems for continuity equations with BV coefficients},
author = {Gianluca Crippa and Carlotta Donadello and Laura V. Spinolo},
journal= {arXiv preprint arXiv:1304.0975},
year = {2013}
}
Comments
25 pages, 5 figures