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Propriétés d’opérateurs de dérivation. Application au problème non homogène de Stokes. (Properties of derivation operators. Application to the nonhomogeneous Stokes’ problem). (French) Zbl 0698.46035

Summary: We give a version of de Rham’s theorem in the spaces \(W^{m,q}\), where m is an integer and \(1<q<\infty\). In particular, this will allow us to give a characterization of distributions by means of their gradient (in the case of bounded domains) and to extend a result due to Nečas. We construct a smooth lifting of boundary values by means of functions with given divergence. This enables us to recover as a special case and to extend Cattabriga’s result on nonhomogeneous Stokes’ problem.

MSC:

46F10 Operations with distributions and generalized functions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E15 Banach spaces of continuous, differentiable or analytic functions
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