Initial–boundary value problems for continuity equations with BV coefficients |
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| Authors: | Gianluca Crippa Carlotta Donadello Laura V Spinolo |
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| Institution: | 1. Departement Mathematik und Informatik, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland;2. Laboratoire de Mathématiques, Université de Franche-Comté, 16 route de Gray, F-25030 Besançon Cedex, France;3. IMATI-CNR, via Ferrata 1, I-27100 Pavia, Italy |
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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 of 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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| Keywords: | 35F16 |
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