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Pré-Publication, Document De Travail Année : 2012

An anisotropic eigenvalue problem of Stekloff type and weighted Wulff inequalities

Résumé

We study the Stekloff eigenvalue problem for the so-called pseudo $p-$Laplacian operator. After proving the existence of an unbounded sequence of eigenvalues, we focus on the first nontrivial eigenvalue $\sigma_{2,p}$, providing various equivalent characterizations for it. We also prove an upper bound for $\sigma_{2,p}$, in terms of geometric quantities. The latter can be seen as the nonlinear analogue of the Brock-Weinstock inequality for the first nontrivial Stekloff eigenvalue of the (standard) Laplacian. Such an estimate is obtained by exploiting a family of sharp weighted Wulff inequalities, which are here derived and appears to be interesting in themselves.
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Dates et versions

hal-00731074 , version 1 (11-09-2012)

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  • HAL Id : hal-00731074 , version 1

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Lorenzo Brasco, Giovanni Franzina. An anisotropic eigenvalue problem of Stekloff type and weighted Wulff inequalities. 2012. ⟨hal-00731074⟩
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