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arXiv · 1612.06230

Some results on Sobolev spaces with respect to a measure and applications to a new transport problem

Jean Louet
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Abstract

We recall some known and present several new results about Sobolev spaces defined with respect to a measure, in particular a precise pointwise description of the tangent space to this measure in dimension 1. This allows to obtain an interesting, original compactness result which stays open in R^d, d \textgreater{} 1, and can be applied to a new transport problem, with gradient penalization.

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Jean Louet. 2016-12-19. Some results on Sobolev spaces with respect to a measure and applications to a new transport problem. https://doi.org/10.1007/s10958-013-1647-4

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