Quelques proprietes des applications de trace dance des espaces de champs de vecteurs a divergence nulle

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Abstract
In many problems arising in cotinuum mechanics, and particularly in the study of icompressible fluids, divergence–free vector fields are used as variational spaces. The boundary conditions met by the weak solutions of such problems are implicitly contained in the variational equation, but the divergence condition makes them very difficult to obtain. We give here a characterization of the traces (in the sense of Sobolev space' theory) of divergence–free vector fields on the boundary of the reference domain; this provides a useful tool to get the above–mentionned boundary conditions, which are necessary at least in the regularity study of solutions.

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