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Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian
Robin Laplacian Eigenvalues Optimisation
2012/4/18
We consider the problem of minimising the $n^{th}-$eigenvalue of the Robin Laplacian in $\mathbb{R}^{N}$. Although for $n=1,2$ and a positive boundary parameter $\alpha$ it is known that the minimiser...
The nodal line of the second eigenfunction of the Robin Laplacian in $\mathbb{R}^2$ can be closed
Laplacian eigenfunction nodal line Robin boundary
2010/12/13
We construct a multiply connected domain in R2 for which the second eigenfunction of the Laplacian with Robin boundary condi-tions has an interior nodal line. In the process, we adapt a bound of Donne...