Amrouche, Chérif 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 C. R. Acad. Sci., Paris, Sér. I 310, No. 6, 367-370 (1990). 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. Cited in 2 Documents 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 Keywords:de Rham’s theorem in the spaces \(W^{m,q}\); characterization of distributions by means of their gradient; smooth lifting of boundary values by means of functions with given divergence; Cattabriga’s result on nonhomogeneous Stokes’ problem PDFBibTeX XMLCite \textit{C. Amrouche}, C. R. Acad. Sci., Paris, Sér. I 310, No. 6, 367--370 (1990; Zbl 0698.46035)