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
;
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.
Articolo in rivista - Articolo scientifico
Asymptotics of Laplacian eigenvalues; Mixed boundary conditions; Monotonicity formula;
English
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315
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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].
Felli, V; Noris, B; Ognibene, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/359097
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