Asymptotic analysis of the eigenvalues of a Laplacian problem in a thin multidomain Antonio GaudielloAli Sili 49R5035P2074K0574K3074K35Laplacian eigenvalue problemthin multidomainsdimension reduction We consider a thin multidomain of $\mathbb{R}^N$, $N \geq 2$, consisting of two vertical cylinders, one placed upon the other: the first one with given height and small cross section, the second one with small thickness and given cross section. In this multidomain we study the asymptotic behavior, when the volumes of the two cylinders vanish, of a Laplacian eigenvalue problem and of a $L^2$-Hilbert orthonormal basis of eigenvectors. We derive the limit eigenvalue problem (which is well posed in the union of the limit domains, with respective dimension $1$ and $N-1$) and the limit basis. We discuss the limit models and we precise how these limits depend on the dimension $N$ and on the limit $q$ of the ratio between the volumes of the two cylinders. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3042 10.1512/iumj.2007.56.3042 en Indiana Univ. Math. J. 56 (2007) 1675 - 1710 state-of-the-art mathematics http://iumj.org/access/