| Abstract: |
| We present a fractional counterpart of a generalized Kohler-Jobin inequality, showing that, among all bounded, open sets $\Omega\subset R^N$ 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 $\lambda_1(\Omega)$. The results have been obtained in collaboration with B. Brandolini, I. de Bonis, G. Piscitelli and B. Volzone. |
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