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We construct a multiply connected domain in $\mathbb{R}^2$ for which thesecond eigenfunction of the Laplacian with Robin boundary conditions has aninterior nodal line. In the process, we adapt a bound of Donnelly-Feffermantype to obtain a uniform estimate on the size of the nodal sets of a sequenceof solutions to a certain class of elliptic equations in the interior of asequence of domains, which does not depend directly on any boundary behaviour.This also gives a new proof of the nodal line property of the example in theDirichlet case.

The nodal line of the second eigenfunction of the Robin Laplacian in $\mathbb{R}^2$ can be closed