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On the tangential set of a nearly incompressible vector field

  • Nikolay Gusev (SISSA Trieste)
Augusteum - A314 Universität Leipzig (Leipzig)

Abstract

In the theory of transport equation arises a problem of representation of a distribution div(β(u)b) where u is a scalar field, b is a vector field with bounded variation and β is a smooth function. Such representation has been obtained by L. Ambrosio, C. De Lellis and J. Maly, up to a singular measure with particular properties. The authors have also obtained a sufficient condition when this measure is zero. In connection with the Bressan's compactness conjecture they have posed a question of existence of a nearly incompressible vector field for which this sufficient condition is not satisfied. An example of such vector field, which has been recently constructed, will be presented.

Anne Dornfeld

MPI for Mathematics in the Sciences Contact via Mail

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