July 1, 2024Open Access

A note on the maximization of the first Dirichlet eigenvalue for perforated planar domains

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Abstract

In this work we prove that given an open bounded set R² with a C² boundary, there exists: = () small enough such that for all 0 < < the maximum of \₁ (- B_{ (x) ): B_ \} is never attained when the ball is close enough to the boundary. In particular it is not obtained when B_ (x) is touching the boundary.

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Manuel Dias (Mon,) studied this question.

synapsesocial.com/papers/68e62289b6db6435875b4452 https://doi.org/https://doi.org/10.48550/arxiv.2407.01237

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3Optimal Domains for Elliptic Eigenvalue Problems with Rough Coefficients2024 · 2 citations
4Type problem, the first eigenvalue and Hardy inequalities2024
5The first Dirichlet eigenvalue and the width2024

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