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| Symmetrization for Fractional Elliptic and Parabolic Equations and an Isoperimetric Application |
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Citation： |
Yannick SIRE,Juan Luis V'AZQUEZ,Bruno VOLZONE.Symmetrization for Fractional Elliptic and Parabolic Equations and an Isoperimetric Application[J].Chinese Annals of Mathematics B,2017,38(2):661~686 |
| Page view： 949
Net amount： 540 |
Authors： |
Yannick SIRE; Juan Luis V'AZQUEZ;Bruno VOLZONE |
Foundation： |
This work was supported by the ANR projects ``HAB'' and
``NONLOCAL'', the Spanish Research Project MTM2011-24696, and the
INDAM-GNAMPA Project 2014 ``Analisi qualitativa di soluzioni di
equazioni ellittiche e di evoluzione'' (Italy). |
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| Abstract： |
This paper develops further the theory of symmetrization of
fractional Laplacian operators contained in recent works of two of
the authors. This theory leads to optimal estimates in the form of
concentration comparison inequalities for both elliptic and
parabolic equations. The authors extend the theory for the so-called
{restricted} fractional Laplacian defined on a bounded domain
$\Omega$ of $\ren$ with zero Dirichlet conditions outside of
$\Omega$. As an application, an original proof of the
corresponding fractional Faber-Krahn inequality is derived. A more
classical variational proof of the inequality is also provided. |
Keywords： |
Symmetrization, Fractional Laplacian, Nonlocal elliptic andparabolic equations, Faber-Krahn inequality |
Classification： |
35B45, 35R11, 35J61, 35K55 |
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