M. V. D. Berg

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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.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…