46 citations · 91 across the 17 of their papers we have counts for
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Regularity in shape optimization under convexity constraint
Jimmy Lamboley, Raphaël Prunier
This paper is concerned with the regularity of shape optimizers of a class of isoperimetric problems under convexity constraint. We prove that minimizers of the sum of the perimete…
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…
Regularity for the optimal compliance problem with length penalization
Antonin Chambolle, Jimmy Lamboley, Antoine Lemenant +1
We prove some regularity results for a connected set S in the planar domain O, which minimizes the compliance of its complement O§, plus its length. This problem, interpreted as to…
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…
Stability in shape optimization with second variation
Marc Dambrine, Jimmy Lamboley, M Dambrine-J
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify struc…