2 papers
math.AP2026
Neumann's nodal line may be closed on doubly-connected planar domains
Pedro Freitas, Roméo Leylekian
We show the existence of planar domains with one hole for which the first non-trivial Neumann eigenfunction has a closed nodal line fully contained inside the domain. This is optim…
math.AP2025
Sharp inequalities and asymptotics for polyharmonic eigenvalues
Davide Buoso, Pedro Freitas
We study eigenvalues of general scalar Dirichlet polyharmonic problems in domains in . We first prove a number of inequalities satisfied by the eigenvalues on genera…