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Sur la trace et le théorème de Stokes dans la théorie des distributions. (On the trace and Stokes’ theorem in the theory of distributions). (French) Zbl 0645.58011

Let X be an n-dimensional manifold piecewise \(C^{\infty}\). Denote by \(\partial_ pX\) a boundary of codimension p, \(p=0,1,...,n\) in X. Then \(X=\partial_ 0X\cup..\cup \partial_ nX\). The author proves the following extension of Stokes’ theorem: Let \(\omega\) be a form- distribution of degree n-1 convergent on \(\partial_ 1X\). Then \(\int_{\partial_ 0X}d\omega =\int_{\partial_ 1X}T_ 1\omega\) where \(T_ 1\omega\) is a certain form on \(\partial_ 1X\) called by the author the trace of \(\omega\) on \(\partial_ 1X\).
Reviewer: W.Mozgawa

MSC:

58C35 Integration on manifolds; measures on manifolds
58A10 Differential forms in global analysis
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