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On some functionals involving torsional rigidity, principal eigenvalue and perimeter

In this paper we study some relationships between the first Dirichlet eigenvalue $Λ(Ω)$ and the torsional rigidity $T(Ω)$ of a domain $Ω$. We consider the problem of optimizing the product $Λ(Ω)T(Ω)$ among sets with prescribed perimeter, both in the class of open sets with finite perimeter and within the class of convex domains. We also present local results for the quantity $Λ(Ω)T(Ω)^q$, with $q>0$, under either a volume or a perimeter constraint.

preprint2026arXivOpen access
Vincenzo AmatoCarlo NitschCristina TrombettiFederico Villone
math.APmath.SP
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Open access4 authors2 topics
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
Citations: 0Reviews: 0Saves: 0Code: not linkedDataset: not linkedInstitutions: 0

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Vincenzo AmatoCarlo NitschCristina TrombettiFederico Villone

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