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

Jean Louet (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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 > 1, and can be applied to a new transport problem, with gradient penalization.

Domaines: Equations aux dérivées partielles [math.AP]

Jean Louet. Some results on Sobolev spaces with respect to a measure and applications to a new transport problem. Journal of Mathematical Sciences, 2014, 196 (2), pp.152 - 164. ⟨10.1007/s10958-013-1647-4⟩. ⟨hal-01419566⟩