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A counterexample to Payne's nodal line conjecture with few holes

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Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoffmann-Ostenhof and Nadirashvili proved this to be false by constructing a counterexample in the plane with many holes and raised the question of the minimum number of holes a counterexample can have. In this paper we prove it is at most 6.

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Communications In Nonlinear Science And Numerical Simulation, 2021, vol. 103, p. 105957

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cc-by-nc-nd (c) Dahne, Joel et al., 2021

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Articles publicats en revistes (Matemàtiques i Informàtica)

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A counterexample to Payne's nodal line conjecture with few holes