M. van den Berg

collaborators

3 papers

math.AP2025

On functionals involving the $p$ -capacity and the $q$ -torsional rigidity

Michiel van den Berg, Nunzia Gavitone

Upper bounds are obtained for the $p$ -capacity of compact sets in $R^{d}$ , with $d \geq 2$ and $1 < p < d$ . Upper and lower bounds are obtained for the product of $p$ -capacity and powers…

math.AP2025

Qualitative properties of the heat content

Michiel van den Berg, Katie Gittins

We obtain monotonicity and convexity results for the heat content of domains in Riemannian manifolds and in Euclidean space subject to various initial temperature conditions. We in…

math.SP2025

On localisation of eigenfunctions of the Laplace operator

Michiel van den Berg, Dorin Bucur

We prove (i) a simple sufficient geometric condition for localisation of a sequence of first Dirichlet eigenfunctions provided the corresponding Dirichlet Laplacians satisfy a unif…

On functionals involving the p-capacity and the q-torsional rigidity

Qualitative properties of the heat content

On localisation of eigenfunctions of the Laplace operator

On functionals involving the $p$ -capacity and the $q$ -torsional rigidity