The hot spots problem in planar domains with one hole
By Krzysztof Burdzy. 2004
62 citations recorded by the source corpus.
There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/90c08768a77bcc59741c363215ff621da43068d8
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In Applied Mathematics
- Mateusz Kwaśnicki
- Tadeusz Kulczycki
- Bartlomiej Siudeja
- Alexander I. Nazarov
- Binh T. Nguyen
- Iosif Polterovich
- Denis S. Grebenkov
- Krzysztof Bogdan
In Computational Theory and Mathematics
- Mateusz Kwaśnicki
- Tadeusz Kulczycki
- Bartlomiej Siudeja
- Alexander I. Nazarov
- Binh T. Nguyen
- Iosif Polterovich
- Denis S. Grebenkov
- Bartłlomiej Dyda
In Mathematical Physics
- Mateusz Kwaśnicki
- Tadeusz Kulczycki
- Bartlomiej Siudeja
- Alexander I. Nazarov
- Binh T. Nguyen
- Iosif Polterovich
- Denis S. Grebenkov
- Bartłlomiej Dyda
Citations in the corpus
- Geometrical Structure of Laplacian Eigenfunctions (2012, background): “This conjecture was proved by Banuelos and Burdzy for a class of planar domains [40], but in general the statement is wrong, as shown by several counterexamples [54, 101, 104, 257].”
- The legacy of Vladimir Andreevich Steklov (2014, background): “It was proved for sufficiently regular planar domains (see, for example, [3] and [26]), disproved for some domains with holes (see, for example, [7]) and is still open for arbitrary convex planar domains.”