23 citations · 41 across the 30 of their papers we have counts for
33 papers
Proof of the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons
Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà
We prove the local version of the Pólya--Szegö conjecture for the torsional rigidity of polygons: for every \(n\geq5\), the regular -gon is a strict local maximizer of torsional…
Symmetry breaking in the polygonal Szegö-Weinberger inequality as : the longest shortest-fence quadrilateral
Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà
We consider Pólya's problem of finding, among convex sets of prescribed area, the one with the longest shortest fence, in the polygonal setting, namely when the class of competitor…
Isoperimetric problems related to extremal diameter graphs in 3D: theoretical and numerical aspects
Beniamin Bogosel
We study optimization problems for separable functionals of the Euclidean or spherical lengths of dual edge pairs in finite extremal unit-diameter configurations in three dimension…
Optimal Finsler-Hadwiger inequalities
Beniamin Bogosel
Various inequalities exist between the area of a triangle, the perimeter squared and the isoperimetric deficit . The direct and reverse Finsl…
Shape optimization under width constraint: the Cheeger constant and the torsional rigidity
Beniamin Bogosel
In this article it is shown that the equilateral triangle maximizes the Cheeger constant and minimizes the torsional rigidity among shapes having a fixed minimal width. The proof t…
Optimisation of space-time periodic eigenvalues
Beniamin Bogosel, Idriss Mazari-Fouquer, Grégoire Nadin
The goal of this paper is to provide a qualitative analysis of the optimisation of space-time periodic principal eigenvalues. Namely, considering a fixed time horizon and the $…
New variational arguments regarding the Blaschke-Lebesgue theorem
Beniamin Bogosel
The sensitivity of the areas of Reuleaux polygons and disk polygons is computed with respect to vertex perturbations. Computations are completed for both constrained and Lagrangian…
Polygonal Faber-Krahn inequality: Local minimality via validated computing
Beniamin Bogosel, Dorin Bucur
The main result of the paper shows that the regular -gon is a local minimizer for the first Dirichlet-Laplace eigenvalue among -gons having fixed area for . Th…
A reverse isoperimetric inequality for convex shapes with inclusion constraint
Beniamin Bogosel
The convex shape contained in a disk having prescribed area and maximal perimeter is completely characterized in terms of the area fraction. The solution is always a polygon having…
Optimization of Neumann Eigenvalues under convexity and geometric constraints
Beniamin Bogosel, Antoine Henrot, Marco Michetti
In this paper we study optimization problems for Neumann eigenvalues among convex domains with a constraint on the diameter or the perimeter. We work mainly in the plane, tho…
Mixed volumes and the Blaschke-Lebesgue theorem
Beniamin Bogosel
The mixed area of a Reuleaux polygon and its symmetric with respect to the origin is expressed in terms of the mixed area of two explicit polygons. This gives a geometric explanati…
Volume computation for Meissner polyhedra and applications
Beniamin Bogosel
The volume of a Meissner polyhedron is computed in terms of the lengths of its dual edges. This allows to reformulate the Meissner conjecture regarding constant width bodies with m…
A Geometric proof for the Polygonal Isoperimetric Inequality
Beniamin Bogosel
Gradients of the perimeter and area of a polygon have straightforward geometric interpretations. The use of optimality conditions for constrained problems and basic ideas in triang…
On the Blaschke-Lebesgue theorem for the Cheeger constant via areas and perimeters of inner parallel sets
Beniamin Bogosel
The first main result presented in the paper shows that the perimeters of inner parallel sets of planar shapes having a given constant width are minimal for the Reuleaux triangles.…
The nonlocal isoperimetric problem for polygons: Hardy-Littlewood and Riesz inequalities
Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà
Given a non-increasing and radially symmetric kernel in , we investigate counterparts of the classical Hardy-Littlewood and Riesz inequa…
On the numerical approximation of Blaschke-Santaló diagrams using Centroidal Voronoi Tessellations
Beniamin Bogosel, Giuseppe Buttazzo, Edouard Oudet
Identifying Blaschke-Santaló diagrams is an important topic that essentially consists in determining the image of a map , where the dimension of the…
Optimization of the Steklov-Lamé eigenvalues with respect to the domain
Beniamin Bogosel, Pedro R. S. Antunes
This work deals with theoretical and numerical aspects related to the behavior of the Steklov-Lamé eigenvalues on variable domains. After establishing the eigenstructure for the di…
On the Polygonal Faber-Krahn Inequality
Beniamin Bogosel, Dorin Bucur
It has been conjectured by Pólya and Szegö seventy years ago that the planar set which minimizes the first eigenvalue of the Dirichlet-Laplace operator among polygons with side…
Numerical shape optimization among convex sets
Beniamin Bogosel
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support fu…
Longest minimal length partitions
Beniamin Bogosel, Edouard Oudet
This article provides numerical evidence that under volume constraint the ball is the set which maximizes the perimeter of the least-perimeter partition into cells with prescribed…
Propagation for KPP bulk-surface systems in a general cylindrical domain
Beniamin Bogosel, Thomas Giletti, Andrea Tellini
In this paper, we investigate propagation phenomena for KPP bulk-surface systems in a cylindrical domain with general section and heterogeneous coefficients. As for the scalar KPP…
Maximization of the Steklov eigenvalues with a diameter constraint
Abdelkader Al Sayed, Beniamin Bogosel, Antoine Henrot +1
In this paper, we address the problem of maximizing the Steklov eigenvalues with a diameter constraint. We provide an estimate of the Steklov eigenvalues for a convex domain in ter…
Parametric Shape Optimization using the Support Function
Pedro R. S. Antunes, Beniamin Bogosel
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate s…
3d positive lattice walks and spherical triangles
B Bogosel, V Perrollaz, K. Raschel +1
In this paper we explore the asymptotic enumeration of three-dimensional excursions confined to the positive octant. As shown in [29], both the exponential growth and the critical…