M. V. D. van den Berg

activity

20102026

most citedHardy inequality and heat semigroup estimates for Riemannian manifolds with singular data

2 citations · 2 across the 5 of their papers we have counts for

collaborators

5 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.AP2021

Intrinsic ultracontractivity for domains in negatively curved manifolds

Hiroaki Aikawa, Michiel van den Berg, Jun Masamune

Let $M$ be a complete, non-compact, connected Riemannian manifold with Ricci curvature bounded from below by a negative constant. A sufficient condition is obtained for open and co…

math.AP2020

On capacity and torsional rigidity

Michiel van den Berg, Giuseppe Buttazzo

We investigate extremality properties of shape functionals which are products of Newtonian capacity $\cp(\overline{\Om})$, and powers of the torsional rigidity $T(\Om)$, for an ope…

math.AP2018

Sign changing solutions of Poisson's equation

Michiel van den Berg, Dorin Bucur

Let $Ω$ be an open, possibly unbounded, set in Euclidean space $R^{m}$ with boundary $\partial Ω,$ let $A$ be a measurable subset of $Ω$ with measure $∣ A ∣$ , and let $γ \in (0, 1)$ . We…

math.SP2010★ 2 cited

Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data

M. van den Berg, P. Gilkey, K. Kirsten +1

Upper bounds are obtained for the heat content of an open set D in a geodesically complete Riemannian manifold M with Dirichlet boundary condition on bd(D), and non-negative initia…