Mickael Nahon

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math.AP2025

Boundary regularity of a fourth order Alt-Caffarelli problem and applications to the minimization of the critical buckling load

Jimmy Lamboley, MickaÃ«l Nahon

We study a higher order analogue to the Alt-Caffarelli functional that arises in several shape optimization problems, among which the minimization of the critical buckling load of…

math.AP2025

Sharp Quantitative Stability of the Dirichlet spectrum near the ball

Dorin Bucur, Jimmy Lamboley, MickaÃ«l Nahon +1

Let $I^c ◯ \subset R^{n}$ be an open set with the same volume as the unit ball $B$ and let $I^»_{k} (I^c ◯)$ be the $k$ -th eigenvalue of the Laplace operator of $I^c ◯$ with Dirichlet boun…

math.AP2025

Spherical caps do not always maximize Neumann eigenvalues on the sphere

Dorin Bucur, Richard S. Laugesen, Eloi Martinet +1

We prove the existence of an open set $I^c ◯ \subset S^{2}$ for which the first positive eigenvalue of the Laplacian with Neumann boundary condition exceeds that of the geodesic…