On Pólya’s Inequality for Torsional Rigidity and First Dirichlet Eigenvalue

Article, Preprint English OPEN
van den Berg, Michiel; Ferone, Vincenzo; Nitsch, Carlo; Trombetti, Cristina;
  • Publisher: Springer Nature
  • Journal: Integral Equations and Operator Theory,volume 86,issue 4,pages579-600 (issn: 0378-620X)
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1007/s00020-016-2334-x
  • Subject: first Dirichlet eigenvalue | Algebra and Number Theory | Mathematics - Analysis of PDEs | Analysis | Torsional rigidity | 49J45, 49R05, 35P15, 47A75, 35J25
    arxiv: Mathematics::Spectral Theory

Let $\Omega$ be an open set in Euclidean space with finite Lebesgue measure $|\Omega|$. We obtain some properties of the set function $F:\Omega\mapsto \R^+$ defined by $$ F(\Omega)=\frac{T(\Omega)\lambda_1(\Omega)}{|\Omega|} ,$$ where $T(\Omega)$ and $\lambda_1(\Omega)$... View more
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