Antoine Henrot, Institut Elie Cartan de Lorraine

Seminar Montreal Analysis Seminar

Université de Montréal, Time and Room TBA

In this talk we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we consider $T(Omega)/(M(Omega)|Omega|)$ and $M(Omega)lambda_1(Omega)$, where $Omega$ is a bounded open set of $mathbb{R}^N$ with finite Lebesgue measure $|Omega|$, $M(Omega)$ denotes the maximum of the torsion function, (solution of $-Delta u=1$ in $Omega$, $u=0$ on the boundary), $T(Omega)=int_Omega u$ $ the torsion, and $lambda_1(Omega)$ the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets.In this talk we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we consider $T(Omega)/(M(Omega)|Omega|)$ and $M(Omega)lambda_1(Omega)$, where $Omega$ is a bounded open set of $mathbb{R}^N$ with finite Lebesgue measure $|Omega|$, $M(Omega)$ denotes the maximum of the torsion function, (solution of $-Delta u=1$ in $Omega$, $u=0$ on the boundary), $T(Omega)=int_Omega u$ $ the torsion, and $lambda_1(Omega)$ the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets.