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On localisation of eigenfunctions of the Laplace operator by Berg, Michiel van den; Bucur, Dorin is a scholarly article available to read on EtoBox.

What is On localisation of eigenfunctions of the Laplace operator about?

We prove (i) a simple sufficient geometric condition for localisation of a sequence of first Dirichlet eigenfunctions provided the corresponding Dirichlet Laplacians satisfy a uniform Hardy inequality, and (ii) localisation of a sequence of first Dirichlet eigenfunctions for a wide class of elongating horn-shaped domains. We give examples of sequences of simply connected, planar, polygonal domains for which the corresponding sequence of first eigenfunctions with either Dirichlet, or Neumann, boundary conditions $\kappa$-localise in $L^2$.

Author

Berg, Michiel van den; Bucur, Dorin

Published

2022

Language

EN