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- W2962832016 abstract "We introduce an analogue of Payne’s nodal line conjecture, which asserts that the nodal (zero) set of any eigenfunction associated with the second eigenvalue of the Dirichlet Laplacian on a bounded planar domain should reach the boundary of the domain. The assertion here is that any eigenfunction associated with the first nontrivial eigenvalue of the Neumann Laplacian on a domain $$Omega $$ with rotational symmetry of order two (i.e. $$xin Omega $$ iff $$-xin Omega $$ ) “should normally” be rotationally antisymmetric. We give both positive and negative results which highlight the heuristic similarity of this assertion to the nodal line conjecture, while demonstrating that the extra structure of the problem makes it easier to obtain stronger statements: it is true for all simply connected planar domains, while there is a counterexample domain homeomorphic to a disk with two holes." @default.
- W2962832016 created "2019-07-30" @default.
- W2962832016 creator A5062799255 @default.
- W2962832016 date "2017-12-07" @default.
- W2962832016 modified "2023-10-12" @default.
- W2962832016 title "A toy Neumann analogue of the nodal line conjecture" @default.
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- W2962832016 doi "https://doi.org/10.1007/s00013-017-1117-1" @default.
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