### Abstract:

We consider the Robin Laplacian in two bounded regions Ω1 and Ω2 of RN with Lipschitz boundaries
and such that Ω2 ⊂ Ω1, and we obtain two-sided estimates for the eigenvalues λn,2 of the Robin
Laplacian in Ω2 via the eigenvalues λn,1 of the Robin Laplacian in Ω1. Our estimates depend on the
measure of the set difference Ω1\Ω2 and on suitably defined characteristics of vicinity of the boundaries
∂Ω1 and ∂Ω2, and of the functions defined on ∂Ω1 and on ∂Ω2 that enter the Robin boundary conditions.

### Description:

We consider the Robin Laplacian in two bounded regions Ω1 and Ω2 of RN with Lipschitz boundaries
and such that Ω2 ⊂ Ω1, and we obtain two-sided estimates for the eigenvalues λn,2 of the Robin
Laplacian in Ω2 via the eigenvalues λn,1 of the Robin Laplacian in Ω1. Our estimates depend on the
measure of the set difference Ω1\Ω2 and on suitably defined characteristics of vicinity of the boundaries
∂Ω1 and ∂Ω2, and of the functions defined on ∂Ω1 and on ∂Ω2 that enter the Robin boundary conditions.