Submitted Paper

Inserted: 26 jul 2025
Last Updated: 2 nov 2025

Pages: 23
Year: 2025

Abstract:

Given the eigenvalue problem for the Laplacian with Robin boundary conditions, (with $\beta\in\mathbb{R}\setminus\{0\}$ the Robin parameter), we consider a shape minimization problem for a function of the first eigenvalues if $\beta>0$ and a shape maximization problem if $\beta<0$. Both problems are settled in a suitable class of generalized polygons with an upper bound on the number of sides, under either perimeter or volume constraint.

Keywords: shape optimization, polygons, Robin laplacian, Geometric control, Higher order eigenvalues

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• CCP_Polygons.pdf