English

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.

Keywords

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

R2 v1 2026-06-21T23:53:05.982Z