37 citations · 81 across the 34 of their papers we have counts for
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Shape optimisation of the maximum of the gradient of the torsion function on convex sets
Michiel van den Berg, Dorin Bucur, Mickael Nahon
We analyse the boundary behaviour of the gradient of the torsion function $w_\Om$ in convex domains $\Om\subset\mathbb{R}^d$. We prove that its -norm is attained at a bou…
Shape optimization with inradius constraint and emergence of honeycomb structures
Dorin Bucur, Giuseppe Buttazzo, Alexis de Villeroché
We maximize the average torsional rigidity among open subsets of with fixed inradius whose complements consist of pairwise disjoint balls of fixed radius $\varepsilo…
Neural networks for spectral optimization
Alexis de Villeroché, Beniamin Bogosel, Stéphane Breuils +2
Given a functional dependent on the spectrum of a differential operator, we address the problem of finding a domain which optimizes this functional. PDE solvers might be used to ta…
Proof of the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons
Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà
We prove the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons: for every \(n\geq5\), the regular -gon is a strict local maximizer of torsional…
Symmetry breaking in the polygonal Szegö-Weinberger inequality as : the longest shortest-fence quadrilateral
Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà
We consider Pólya's problem of finding, among convex sets of prescribed area, the one with the longest shortest fence, in the polygonal setting, namely when the class of competitor…