Author

D. Bucur

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Preprint Oct 2026

Shape optimisation of the maximum of the gradient of the torsion function on convex sets

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 $L^\infty$-norm is attained at a boundary point and establish the stability of this norm under general (convex) perturbations. For problems of the form $$\sup\{\|\nabla w_{\Om}...

M. J. Van den Berg, D. Bucur, Mickael Nahon · 0 citations

Preprint Sep 2026

Proof of the local version of the P\'olya--Szeg\"o conjecture for the torsional rigidity of polygons

We prove the local version of the P\'olya--Szeg\"o conjecture for the torsional rigidity of polygons: for every $n\geq5$, the regular $n$-gon is a strict local maximizer of torsional rigidity among convex $n$-gons of prescribed area. Our proof is entirely analytic. It builds on a locally stable proportional triangula...

Beniamin Bogosel, D. Bucur, Ilaria Fragalà · 0 citations

#artificial intelligence Preprint Sep 2026

Neural networks for spectral optimization

Two neural network models are proposed which learn the spectrum directly from the geometry of the domain and can be used to optimize the domain from one or more eigenvalues, and which produce accurate differentiable estimates of eigenvalues, which can be used in shape optimization problems involving spectral quantities...

A. de-Villeroche, Beniamin Bogosel, Stéphane Breuils et al. · 0 citations