Author

Mickael Nahon

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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

Optimal regularity for vectorial, higher order and non-minimizing Bernoulli problems

We prove the Lipschitz regularity of solutions for a wide class of generalized Bernoulli free boundary problems, in vectorial, higher order, and non-minimizing settings. Our method does not rely on notions of viscosity solutions or comparison methods, which allows us to reach the optimal regularity for Bernoulli-type p...

G. De Philippis, Jonas Hirsch, Mickael Nahon · 1 citation