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arXiv · 2512.17400

First Eigenvalue and Torsional Rigidity: Isoperimetric Inequalities for the Fractional Laplacian

Barbara Brandolini·Ida de Bonis·Vincenzo Ferone·Gianpaolo Piscitelli·Bruno Volzone
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Abstract

We present a fractional counterpart of a generalized Kohler-Jobin inequality, showing that, among all bounded, open sets $\Omega\subset \mathbb{R}^N$ with Lipschitz boundary, having the same fractional torsional rigidity, the first Dirichlet eigenvalue $\lambda_1(\Omega)$ of the fractional Laplacian attains its minimum on balls. With the same arguments we also establish a reverse H\"older inequality for an eigenfunction corresponding to $\lambda_1(\Omega)$.

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Barbara Brandolini, Ida de Bonis, Vincenzo Ferone, Gianpaolo Piscitelli, Bruno Volzone. 2025-12-19. First Eigenvalue and Torsional Rigidity: Isoperimetric Inequalities for the Fractional Laplacian. https://arxiv.org/abs/2512.17400

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