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math.AP2026
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…
math.AP2026
Optimal regularity for vectorial, higher order and non-minimizing Bernoulli problems
Guido De Philippis, Jonas Hirsch, Mickaël Nahon
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…