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arXiv:1304.0975 [math.AP]AbstractReferencesReviewsResources

Initial-boundary value problems for continuity equations with BV coefficients

Gianluca Crippa, Carlotta Donadello, Laura V. Spinolo

Published 2013-04-03Version 1

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.

Comments: 25 pages, 5 figures
Categories: math.AP
Subjects: 35F16
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