Weyl formula with optimal remainder estimate of some elastic networks and applications
Bulletin de la Société Mathématique de France, Volume 138 (2010) no. 3, pp. 395-413.

We consider a network of vibrating elastic strings and Euler-Bernoulli beams. Using a generalized Poisson formula and some Tauberian theorem, we give a Weyl formula with optimal remainder estimate. As a consequence we prove some observability and stabilization results.

Nous considérons un réseau de cordes et de poutres d'Euler-Bernoulli. En utilisant une formule de Poisson généralisée et un théorème taubérien nous prouvons une formule de Weyl avec reste optimal. Comme conséquence nous prouvons des résultats d'observabilités et de stabilisations.

DOI: 10.24033/bsmf.2593
Classification: 35P20,  93D15,  93D20
Keywords: networks of strings, networks of Euler-Bernoulli beams, tauberian theorem, Weyl formula
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     title = {Weyl formula with optimal remainder estimate of some elastic networks and applications},
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Ammari, Kaïs; Dimassi, Mouez. Weyl formula with optimal remainder estimate of some elastic networks and applications. Bulletin de la Société Mathématique de France, Volume 138 (2010) no. 3, pp. 395-413. doi : 10.24033/bsmf.2593. http://www.numdam.org/articles/10.24033/bsmf.2593/

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