We present a fractional counterpart of a generalized Kohler-Jobin inequality, showing that, among all bounded, open sets Ω⊂ℝN with Lipschitz boundary, having the same fractional torsional rigidity, the first Dirichlet eigenvalue λ1(Ω) of the fractional Laplacian attains its minimum on balls. With the same arguments we also establish a reverse Hölder inequality for an eigenfunction corresponding to λ1(Ω).
First Eigenvalue and Torsional Rigiditiy: Isoperimetric Inequalities for the Fractional Laplacian
G. Piscitelli;
In corso di stampa
Abstract
We present a fractional counterpart of a generalized Kohler-Jobin inequality, showing that, among all bounded, open sets Ω⊂ℝN with Lipschitz boundary, having the same fractional torsional rigidity, the first Dirichlet eigenvalue λ1(Ω) of the fractional Laplacian attains its minimum on balls. With the same arguments we also establish a reverse Hölder inequality for an eigenfunction corresponding to λ1(Ω).File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
