Let $Omega$ be a bounded open set of $mathbb R^n$, $nge 2$. In this paper we mainly study some properties of the second Dirichlet eigenvalue $lambda_2(p,Omega)$ of the anisotropic $p$-Laplacian [ -mathcal Q_pu:=- extrmdiv left(F^p-1( abla u)F_\xi ( abla u) ight), ] where $F$ is a suitable smooth norm of $mathbb R^n$ and $pin]1,+infty[$. We provide a lower bound of $lambda_2(p,Omega)$ among bounded open sets of given measure, showing the validity of a Hong-Krahn-Szego type inequality. Furthermore, we investigate the limit problem as $p o+infty$.
On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators / DELLA PIETRA, Francesco; Gavitone, Nunzia; Piscitelli, Gianpaolo. - In: BULLETIN DES SCIENCES MATHEMATIQUES. - ISSN 0007-4497. - 155:(2019), pp. 10-32. [10.1016/j.bulsci.2019.02.005]
On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators
Della Pietra Francesco
;Gavitone Nunzia;Piscitelli Gianpaolo
2019
Abstract
Let $Omega$ be a bounded open set of $mathbb R^n$, $nge 2$. In this paper we mainly study some properties of the second Dirichlet eigenvalue $lambda_2(p,Omega)$ of the anisotropic $p$-Laplacian [ -mathcal Q_pu:=- extrmdiv left(F^p-1( abla u)F_\xi ( abla u) ight), ] where $F$ is a suitable smooth norm of $mathbb R^n$ and $pin]1,+infty[$. We provide a lower bound of $lambda_2(p,Omega)$ among bounded open sets of given measure, showing the validity of a Hong-Krahn-Szego type inequality. Furthermore, we investigate the limit problem as $p o+infty$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
