preprint

Inserted: 17 mar 2023

Year: 2023

Abstract:

We prove an improved Pleijel nodal domain theorem for the Robin eigenvalue problem. In particular we remove the restriction, imposed in previous work, that the Robin parameter be non-negative. We also improve the upper bound in the statement of the Pleijel theorem. In the particular example of a Euclidean ball, we calculate the explicit value of the Pleijel constant for a generic constant Robin parameter and we show that it is equal to the Pleijel constant for the Dirichlet Laplacian on a Euclidean ball.