4 citations · 6 across the 12 of their papers we have counts for
12 papers
Localisation for the torsion function and the strong Hardy inequality
Michiel van den Berg, Thomas Kappeler
Two-sided bounds for the efficiency of the torsion function are obtained in terms of the square of the distance to the boundary function under the hypothesis that the Dirichlet Lap…
On the relations between principal eigenvalue and torsional rigidity
Michiel van den Berg, Giuseppe Buttazzo, Aldo Pratelli
We consider the problem of minimising or maximising the quantity on the class of open sets of prescribed Lebesgue measure. Here is fixed, denotes the firs…
Heat flow from polygons
Michiel van den Berg, Peter Gilkey, Katie Gittins
We study the heat flow from an open, bounded set in with a polygonal boundary . The initial condition is the indicator function of . A Dirichlet bound…
On a Pólya functional for rhombi, isosceles triangles, and thinning convex sets
M. van den Berg, V. Ferone, C. Nitsch +1
Let be an open convex set in with finite width, and let be the torsion function for , i.e. the solution of . An upper bound is ob…
On the norm of the torsion unction
Michiel van den Berg, Thomas Kappeler
Bounds are obtained for the norm of the torsion function , i.e. the solution of in terms of the Lebesgue measure of and the principal eigen…
Neumann heat content asymptotics with singular initial temperature and singular specific heat
M. van den Berg, P. Gilkey, H. Kang
We study the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions i…