3 citations · 3 across the 11 of their papers we have counts for
15 papers
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…
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…
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…
Computation of harmonic functions on higher genus surfaces
Mickaël Nahon, Édouard Oudet
We extend a classical approximation result of harmonic functions in planar domains due to Bernstein and Walsch to the setting of harmonic functions in Riemann surfaces. This result…
Minimality of vortex solutions to Ginzburg--Landau type systems for gradient fields in the unit ball in dimension
Radu Ignat, Mickael Nahon, Luc Nguyen
We prove that the degree-one vortex solution is the unique minimizer for the Ginzburg--Landau functional for gradient fields (that is, the Aviles--Giga model) in the unit ball $B^N…
Sharp Quantitative Stability of the Dirichlet spectrum near the ball
Dorin Bucur, Jimmy Lamboley, Mickaël Nahon +1
Let be an open set with the same volume as the unit ball and let be the -th eigenvalue of the Laplace operator of with Dirichlet boundary…
A free discontinuity approach to optimal profiles in Stokes flows
Dorin Bucur, Antonin Chambolle, Alessandro Giacomini +1
In this paper we study obstacles immerged in a Stokes flow with Navier boundary conditions. We prove the existence and regularity of an obstacle with minimal drag, among all shapes…
Sharp inequalities for Neumann eigenvalues on the sphere
Dorin Bucur, Eloi Martinet, Mickaël Nahon
We prove that the second nontrivial Neumann eigenvalue of the Laplace-Beltrami operator on the unit sphere is maximized by the union of tw…
Boundary behavior of Robin problems in non-smooth domains
Dorin Bucur, Alessandro Giacomini, Mickaël Nahon
We analyze strict positivity at the boundary for nonnegative solutions of Robin problems in general (non-smooth) domains, e.g. open sets with rectifiable topological boundaries hav…
Shape optimization of a thermal insulation problem
Dorin Bucur, Mickaël Nahon, Carlo Nitsch +1
We study a shape optimization problem involving a solid that is maintained at constant temperature and is enveloped by a layer of insulating material whi…
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.…
Existence and regularity of optimal shapes for spectral functionals with Robin boundary conditions
Mickaël Nahon
We establish the existence and find some qualitative properties of open sets that minimize functionals of the form under measure constraint on , wh…
Degenerate free discontinuity problems and spectral inequalities in quantitative form
Dorin Bucur, Alessandro Giacomini, Mickaël Nahon
We introduce a new geometric-analytic functional that we analyse in the context of free discontinuity problems. Its main feature is that the geometric term (the length of the jump…
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…