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arXiv · 1304.0975

Initial-boundary value problems for continuity equations with BV coefficients

Gianluca Crippa·Carlotta Donadello·Laura V. Spinolo
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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.

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Gianluca Crippa, Carlotta Donadello, Laura V. Spinolo. 2013-04-03. Initial-boundary value problems for continuity equations with BV coefficients. https://arxiv.org/abs/1304.0975

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