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.
Felli, V., Noris, B., Ognibene, R. (2022). Eigenvalues of the Laplacian with moving mixed boundary conditions: The case of disappearing Neumann region. JOURNAL OF DIFFERENTIAL EQUATIONS, 320(25 May 2022), 247-315 [10.1016/j.jde.2022.02.052].
Eigenvalues of the Laplacian with moving mixed boundary conditions: The case of disappearing Neumann region
Felli, Veronica
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2022
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.
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