M. V. D. Berg

collaborators

3 papers

math.AP2026

On the gradient of the torsion function for elongated cylinders

Michiel van den Berg

Let $(0, L) \times E_{a} \subset R^{d + 1}$ denote the cylinder of length $L$ , and base $E_{a} \subset R^{d},$ where $E_{a}$ is an open ellipsoid with semi-axes $a = (a_{1}, ..., a_{d})$ . Let $w_{(0…

math.SP2024

On the torsion function for simply connected, open sets in $R^{2}$

Michiel van den Berg, Dorin Bucur

For an open set $\Om \subset \R^2$ let $Î»(\Om)$ denote the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Om)$. Let $w_\Om$ be the torsion function for $\Om$, a…

math.AP2024

On some isoperimetric inequalities for the Newtonian capacity

Michiel van den Berg

Upper bounds are obtained for the Newtonian capacity of compact sets in $R^{d}, d \geq 3$ in terms of the perimeter of the $r$ -parallel neighbourhood of $K$ . For compact, convex sets…

On the gradient of the torsion function for elongated cylinders

On the torsion function for simply connected, open sets in R2

On some isoperimetric inequalities for the Newtonian capacity

On the torsion function for simply connected, open sets in $R^{2}$