13 citations · 13 across the 5 of their papers we have counts for
8 papers
On the torsion function for simply connected, open sets in
Michiel van den Berg, Dorin Bucur
For an open set $\Om \subset \R^2$ let $λ(\Om)$ denote the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Om)$. Let $w_\Om$ be the torsion function for $\Om$, an…
On some isoperimetric inequalities for the Newtonian capacity
Michiel van den Berg
Upper bounds are obtained for the Newtonian capacity of compact sets in in terms of the perimeter of the -parallel neighbourhood of . For compact, convex sets…
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 some variational problems involving capacity, torsional rigidity, perimeter and measure
Michiel van den Berg, Andrea Malchiodi
We investigate the existence of a maximiser among open, bounded, convex sets in for the product of torsional rigidity and Newtonian capacity (or logarithmic capacit…
On efficiency and localisation for the torsion function
M. van den Berg, D. Bucur, T. Kappeler
We consider the torsion function for the Dirichlet Laplacian , and for the Schrödinger operator on an open set of finite Lebesgue measure $0<|Ω|<\infty…
Efficiency and localisation for the first Dirichlet eigenfunction
Michiel van den Berg, Francesco Della Pietra, Giuseppina Di Blasio +1
Bounds are obtained for the efficiency or mean to peak ratio for the first Dirichlet eigenfunction (positive) for open, connected sets with finite measure in Euclidean s…