Search

Abstract: Let Ω be an opened domain of with a boundary Γ. The problem numbered (1) in the text has a unique solution in , if , on a part of Γ the area S of which is different from zero and . ɛ is the damping of an elastic structure and ζ is the normalised acoustic impedance of the internal wall of the cavity. ɛ and are small parameters. Thanks to a proper modal expansion and a mean over a narrow band of wave number k, an integral relation between the trace of u on and g is built to the first order in and ɛ, using the residues theorem. It is not an equivalent equation to the problem, but just a step towards its resolution, which will be published in future papers. To cite this article: D. Brenot, C. R. Acad. Sci. Paris, Ser. I 340 (2005). [Copyright &y& Elsevier]

Abstract: Let T be a closed positive current of dimension p in and H an analytic subvariety of of dimension . We denote by the slice of T in H if it exists. We consider the functions on defined by and . The aim of this paper is to establish relationship between the growth of these functions. We prove results generalizing those of L. Gruman in [Séminaire Lelong–Skoda 1981–1983, Lecture Notes in Math., vol. 1028, Springer-Verlag, Berlin, 1983, pp. 125–162] and B. Molzan, B. Shiffman and N. Sibony in [Math. Ann. 257 (1981) 43]. [Copyright &y& Elsevier]