Reverse Faber-Krahn inequality for a truncated Laplacian operator
Parini, Enea (Aix-Marseille Université)
Rossi, Julio D. (Universidad de Buenos Aires. Departamento de Matemática)
Salort, Ariel (Universidad de Buenos Aires. Departamento de Matemática)

Date:	2022
Abstract:	In this paper we prove a reverse Faber-Krahn inequality for the principal eigenvalue µ1(Ω) of the fully nonlinear eigenvalue problem (−λN (D2u) = µu in Ω,u = 0 on ∂Ω. Here λN (D2u) stands for the largest eigenvalue of the Hessian matrix of u. More precisely, we prove that, for an open, bounded, convex domain Ω ⊂ RN , the inequality µ1(Ω) ≤π2[diam(Ω)]2= µ1(Bdiam(Ω)/2), where diam(Ω) is the diameter of Ω, holds true. The inequality actually implies a stronger result, namely, the maximality of the ball under a diameter constraint. Furthermore, we discuss the minimization of µ1(Ω) under different kinds of constraints.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Truncated laplacian ; Reverse faber-krahn inequality ; Spectral optimization
Published in:	Publicacions matemàtiques, Vol. 66 Núm. 2 (2022) , p. 441-455 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/402225
DOI: 10.5565/PUBLMAT6622201

15 p, 343.5 KB

The record appears in these collections:
Articles > Published articles > Publicacions matemàtiques
Articles > Research articles