Optimizing the ground of a Robin Laplacian: asymptotic behavior

Pavel Exner; Hynek Kovarik

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arXiv · 2408.11636

Optimizing the ground of a Robin Laplacian: asymptotic behavior

Pavel Exner·Hynek Kovarik

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Abstract

In this note we consider achieving the largest principle eigenvalue of a Robin Laplacian on a bounded domain $\Omega$ by optimizing the Robin parameter function under an integral constraint. The main novelty of our approach lies in establishing a close relation between the problem under consideration and the asymptotic behavior of the Dirichlet heat content of $\Omega$. By using this relation we deduce a two-term asymptotic expansion of the principle eigenvalue and discuss several applications.

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BibTeX RIS

Pavel Exner, Hynek Kovarik. 2024-08-21. Optimizing the ground of a Robin Laplacian: asymptotic behavior. https://arxiv.org/abs/2408.11636

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