It is known that, if $\Omega\subset\R^2$ is a convex, possibly unbounded, set, then the first nontrivial Neumann eigenvalue of the Hermite operator satisfies the following inequality: $\mu_1(\Omega)\ge 1$. We investigate the equality case, by proving that $\mu_1(\Omega)=1$ if and only if $\Omega$ is a strip.
The equality case in a Poincarè-Wirtinger inequality / Brandolini, B.. - (2018). (Intervento presentato al convegno 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications tenutosi a Taipei (Taiwan) nel 5-9 luglio 2018).
The equality case in a Poincarè-Wirtinger inequality
B. Brandolini
2018
Abstract
It is known that, if $\Omega\subset\R^2$ is a convex, possibly unbounded, set, then the first nontrivial Neumann eigenvalue of the Hermite operator satisfies the following inequality: $\mu_1(\Omega)\ge 1$. We investigate the equality case, by proving that $\mu_1(\Omega)=1$ if and only if $\Omega$ is a strip.File in questo prodotto:
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