A concentric ball is a strictly stable local minimizer for the two-phase Robin eigenvalue under volume constraint if and only if the eigenvalue is below the principal Neumann eigenvalue of the inner ball.
On the optimal shape of a thin insulating layer
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As the layer thickness parameter ε tends to zero, the spectrum of the elliptic operator on the extended domain converges to the spectrum on Ω, accompanied by a first-order asymptotic development.
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Symmetry-breaking and local stability of a two-phase eigenvalue problem in optimal insulation
A concentric ball is a strictly stable local minimizer for the two-phase Robin eigenvalue under volume constraint if and only if the eigenvalue is below the principal Neumann eigenvalue of the inner ball.
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Remarks on the reinforcement of the spectrum of an elliptic problem with Robin boundary condition
As the layer thickness parameter ε tends to zero, the spectrum of the elliptic operator on the extended domain converges to the spectrum on Ω, accompanied by a first-order asymptotic development.