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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, Mickaël 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
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 for which the first positive eigenvalue of the Laplacian with Neumann boundary condition exceeds that of the geodesic d…