Konferenzvortragsdetails

Konferenz: Workshop on the occasion of Erwin Bolthausen's 70th birthday


On Pólya’s inequality for torsional rigidity and first Dirichlet eigenvalue

Vortrag von Prof. Dr. Michiel van den Berg
Datum: 15.09.16   Zeit: 14.20 - 15.10   Raum: Y16G05

Let $\Omega $ be an open set in Euclidean space with finite Lebesgue measure $|\Omega |$. We obtain some properties of the set function $F : \Omega \rightarrow {\mathbb R}^+ $ defined by

$$ F(\Omega ) = \frac{T(\Omega ) \lambda _1(\Omega)}{|\Omega |} ,$$

where $T(\Omega )$ and $\lambda_1(\Omega )$ are the torsional rigidity and first eigenvalue of the Dirichlet Laplacian respectively. For any $m = 2, 3, \ldots $ and $\epsilon \in (0, 1)$ we construct an open set $\Omega _\epsilon \subset {\mathbb R}^m$ such that $F(\Omega _\epsilon ) \geq 1 - \epsilon $.

This is joint work with Enzo Ferone, Carlo Nitsch and Cristina Trombetti.