A counterexample to Payne’s nodal line conjecture with few holes
نویسندگان
چکیده
Payne conjectured in 1967 that the nodal line of second Dirichlet eigenfunction must touch boundary domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof, Hoffmann-Ostenhof and Nadirashvili proved this to be false by constructing a counterexample plane with many holes raised question minimum number can have. paper we prove it is at most 6.
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ژورنال
عنوان ژورنال: Communications in Nonlinear Science and Numerical Simulation
سال: 2021
ISSN: ['1878-7274', '1007-5704']
DOI: https://doi.org/10.1016/j.cnsns.2021.105957