Calculus of Variations and Geometric Measure Theory

V. Felli - B. Noris - R. Ognibene

Eigenvalues of the Laplacian with moving mixed boundary conditions: the case of disappearing Neumann region

created by ognibene on 15 Oct 2021
modified on 25 Mar 2023


Published Paper

Inserted: 15 oct 2021
Last Updated: 25 mar 2023

Journal: Journal of Differential Equations
Year: 2021

ArXiv: 2107.03862 PDF


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.