Work

On Some Functionals Involving Torsional Rigidity, Principal Eigenvalue and Perimeter

Year: 2026

Type: article

Abstract: In this paper we study some relationships between the first Dirichlet Laplacian eigenvalue $$\Lambda (\Omega )$$ Λ ( Ω ) and the torsional rigidity $$T(\Omega )$$ T ( Ω ) of a domain $$\Omega $$ Ω . We consider the problem of optimizing the product $$\Lambda (\Omega )T(\Omega )$$ Λ ( Ω ) T ( Ω ) among sets with prescribed perimeter, both in the class of open sets with finite perimeter and within the class of convex domains. We also characterize the values of $$q>0$$ q > 0 for which the ball is a stable local minimizer or maximizer of the quantity $$\Lambda (\Omega )T(\Omega )^q$$ Λ ( Ω ) T ( Ω ) q , under either a volume or a perimeter constraint.

Source: Potential Analysis

DOI: 10.1007/s11118-026-10328-2

Authors: Vincenzo Amato, Carlo Nitsch, Cristina Trombetti, Federico Villone

Institutions: Scuola Superiore Meridionale, University of Naples Federico II

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni