University of Birmingham > Talks@bham > Topology and Dynamics Seminar > On PoincarĂ© inequalities and counting functions on 1-foliated domains with fractal boundaries (Part II)

On Poincaré inequalities and counting functions on 1-foliated domains with fractal boundaries (Part II)

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The basic necessary notions to understand the variational formulation of eigenvalue problems of a Laplace operator with Neumann boundary conditions are introduced. We summarise some known results (in particular the Weyl-Berry conjecture and related results). A constructive method to obtain estimates for Poincaré constants on certain domains with fractal boundary is developed by introducing specific 1-foliations on the domain. This is used to estimate eigenvalue counting functions for domains with rough boundary and in particular for snowflake-like domains.

This talk is part of the Topology and Dynamics Seminar series.

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