25 citations · 51 across the 8 of their papers we have counts for
9 papers
Polygons as maximizers of Dirichlet energy or first eigenvalue of Dirichlet-Laplacian among convex planar domains
Jimmy Lamboley, Arian Novruzi, Michel Pierre
In this paper we prove that solutions to several shape optimization problems in the plane, with a convexity constraint on the admissible domains, are polygons. The main terms of th…
Regularity of Minimizers of Shape Optimization Problems involving Perimeter
Guido De Philippis, Jimmy Lamboley, Michel Pierre +1
We prove existence and regularity of optimal shapes for the problemwhere denotes the perimeter, is the vo…
Global wellposedness for a class of reaction-advection-anisotropic-diffusion systems
Dieter Bothe, André Fischer, Michel Pierre +1
We prove existence and uniqueness of global solutions for a class of reaction-advection-anisotropic-diffusion systems whose reaction terms have a "triangular structure". We thus ex…
Estimates of First and Second Order Shape Derivatives in Nonsmooth Multidimensional Domains and Applications
Jimmy Lamboley, Arian Novruzi, Michel Pierre
In this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDE's around nonsmooth domains, ess…
Global existence for diffusion-electromigration systems in space dimension three and higher
Dieter Bothe, André Fischer, Michel Pierre +1
We prove existence of global weak solutions for the Nernst-Planck-Poisson problem which describes the evolution of concentrations of charged species subject to Fick…
Global well-posedness of a conservative relaxed cross diffusion system
Thomas Lepoutre, Michel Pierre, Guillaume Rolland
We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form $u_i\to \partial_tu_i-Δ(a_i(\tilde{u})u_i…