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Pré-Publication, Document De Travail Année : 2015

Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application

Résumé

We develop further the theory of symmetrization of fractional Laplacian operators contained in recent works of two of the authors. The theory leads to optimal estimates in the form of concentration comparison inequalities for both elliptic and parabolic equations. In this paper we extend the theory for the so-called \emph{restricted} fractional Laplacian defined on a bounded domain $\Omega$ of $\mathbb R^N$ with zero Dirichlet conditions outside of $\Omega$. As an application, we derive an original proof of the corresponding fractional Faber-Krahn inequality. We also provide a more classical variational proof of the inequality.

Dates et versions

hal-01341894 , version 1 (05-07-2016)

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Yannick Sire, Juan Luis Vazquez, Bruno Volzone. Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application. 2015. ⟨hal-01341894⟩
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