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math.AP2019
Asymptotic behavior of -capacities and singular perturbations for the Dirichlet-Laplacian
Laura Abatangelo, Virginie Bonnaillie-Noël, Corentin Léna +1
In this paper we study the asymptotic behavior of -capacities of small sets and its application to the analysis of the eigenvalues of the Dirichlet-Laplacian on a bounded planar…
math.AP2018
Eigenvalue variation under moving mixed Dirichlet-Neumann boundary conditions and applications
Laura Abatangelo, Veronica Felli, Corentin Léna
We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet-Neumann boundary conditions. In case of simple eigenvalues, we compute…
math.AP2015
On the parity of the number of nodal domains for an eigenfunction of the Laplacian on tori
Corentin Léna
In this note, we discuss a question posed by T. Hoffmann-Ostenhof concerning the parity of the number of nodal domains for a non-constant eigenfunction of the Laplacian on flat tor…