On Polya's inequality for torsional rigidity and first Dirichlet eigenvalue

Article, Preprint English OPEN
Berg, M. van den ; Ferone, V. ; Nitsch, C. ; Trombetti, C. (2016)
  • Publisher: Springer Nature
  • Journal: volume 86, pages 579-600 (issn: 0378-620X)
  • Related identifiers: doi: 10.1007/s00020-016-2334-x, doi: 10.13039/501100000883
  • Subject: Algebra and Number Theory | first Dirichlet eigenvalue | 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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