Published Paper

Inserted: 15 oct 2021
Last Updated: 24 jan 2025

Journal: Journal of Differential Equations
Year: 2022
Doi: https://doi.org/10.1016/j.jde.2022.02.052

Abstract:

We deal with eigenvalue problems for the Laplacian with varying mixed boundary conditions, consisting in homogeneous Neumann conditions on a vanishing portion of the boundary and Dirichlet conditions on the complement. By the study of an Almgren type frequency function, we derive upper and lower bounds of the eigenvalue variation and sharp estimates in the case of a strictly star-shaped Neumann region.