most citedAsymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case

38 citations · 60 across the 3 of their papers we have counts for

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3 papers

math.AP2006★ 38 cited

Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case

Youcef Amirat, Gregory A. Chechkin, Rustem R. Gadyl'shin

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue o…

math.AP2006★ 13 cited

Asymptotic behaviour of the inductance coefficient for thin conductors

Rachid Touzani, Youcef Amirat

We study the asymptotic behaviour of the inductance coefficient for a thin toroidal inductor whose thickness depends on a small parameter $\eps>0$. We give an explicit form of the…

math.AP2006★ 9 cited

A Two-dimensional eddy current model using thin inductors

Youcef Amirat, Rachid Touzani

We derive a mathematical model for eddy currents in two dimensional geometries where the conductors are thin domains. We assume that the current flows in the -direction and t…