Calculus of Variations and Geometric Measure Theory

A. Hassannezhad - D. Sher

On Pleijel's nodal domain theorem for the Robin problem

created by hassannezhad1 on 17 Mar 2023



Inserted: 17 mar 2023

Year: 2023

ArXiv: 2303.08094 PDF


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.