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 compariso...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 Ω of R^N with zero Dirichlet conditions outside of Ω. 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.展开更多
基金supported by the ANR projects“HAB”and“NONLOCAL”,the Spanish Research Project MTM2011-24696the INDAM-GNAMPA Project 2014“Analisi qualitativa di soluzioni di equazioni ellittiche e di evoluzione”(Italy)
文摘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 Ω of R^N with zero Dirichlet conditions outside of Ω. 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.
