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arXiv · 2307.12889

Estimates on the Neumann and Steklov principal eigenvalues of collapsing domains

Paolo Acampora·Vincenzo Amato·Emanuele Cristoforoni
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Abstract

We investigate the relationship between the Neumann and Steklov principal eigenvalues emerging from the study of collapsing convex domains in $\mathbb{R}^2$. Such a relationship allows us to give a partial proof of a conjecture concerning estimates of the ratio of the former to the latter: we show that thinning triangles maximize the ratio among convex thinning sets, while thinning rectangles minimize the ratio among convex thinning with some symmetry property.

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Paolo Acampora, Vincenzo Amato, Emanuele Cristoforoni. 2023-07-24. Estimates on the Neumann and Steklov principal eigenvalues of collapsing domains. https://doi.org/10.1142/s0219199725500270

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