Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4611704 | Journal of Differential Equations | 2011 | 19 Pages |
Abstract
We construct a multiply connected domain in R2 for which the second eigenfunction of the Laplacian with Robin boundary conditions has an interior nodal line. In the process, we adapt a bound of Donnelly–Fefferman type to obtain a uniform estimate on the size of the nodal sets of a sequence of solutions to a certain class of elliptic equations in the interior of a sequence 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 the Dirichlet case.
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Physical Sciences and Engineering
Mathematics
Analysis