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Interaction of concentrated masses in a harmonically oscillating spatial body with Neumann boundary conditions. (English) Zbl 0791.35090
The author considers a Neumann eigenvalue problem of the type \[ \Delta u+ \lambda\gamma (\varepsilon,x) u=0 \quad\text{in } \Omega\subset \mathbb{R}^ 3, \qquad \partial u/\partial\gamma= 0 \quad \text{on }\partial\Omega. \] Here the “weight-function” \(\gamma(\varepsilon,x)\) describes masses, concentrated in some points of \(\Omega\), as \(\varepsilon\to 0\). The asymptotic behaviour of this eigenvalue problem is then investigated.
Reviewer: R.Sperb (Zürich)

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
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