4 papers
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…
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…
Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces
Mikhail Karpukhin, Mickaël Nahon, Iosif Polterovich +1
We prove stability estimates for the isoperimetric inequalities for the first and the second nonzero Laplace eigenvalues on surfaces, both globally and in a fixed conformal class.…
A new continuum theory for incompressible swelling materials
Pierre Degond, Marina A. Ferreira, Sara Merino-Aceituno +1
Swelling media (e.g. gels, tumors) are usually described by mechanical constitutive laws (e.g. Hooke or Darcy laws). However, constitutive relations of real swelling media are not…