25 citations · 26 across the 8 of their papers we have counts for
5 papers · 1 filter
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…
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…
Modeling, shape analysis and computation of the equilibrium pore shape near a PEM-PEM intersection
Peter Berg, Sven-Joachim Kimmerle, Arian Novruzi
In this paper we study the equilibrium shape of an interface that represents the lateral boundary of a pore channel embedded in an elastomer. The model consists of a system of PDEs…
Regularity and singularities of Optimal Convex shapes in the plane
Jimmy Lamboley, Michel Pierre, Arian Novruzi
We focus here on the analysis of the regularity or singularity of solutions $\Om_{0}$ to shape optimization problems among convex planar sets, namely: $$ J(\Om_{0})=\min\{J(\Om),\…
Polygons as optimal shapes with convexity constraint
Jimmy Lamboley, Arian Novruzi
In this paper, we focus on the following general shape optimization problem: $$ \min\{J(\Om), \Om convex, \Om\in\mathcal S_{ad}\}, $$ where is a set of 2-dimensio…