Dorin Bucur

activity

20142024

collaborators

6 papers

math.NA2024

Polygonal Faber-Krahn inequality: Local minimality via validated computing

Beniamin Bogosel, Dorin Bucur

The main result of the paper shows that the regular $n$ -gon is a local minimizer for the first Dirichlet-Laplace eigenvalue among $n$ -gons having fixed area for $n \in {5, 6}$ . Th…

math.OC2023

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 $L_{loc}^{1} (R^{2}; R_{+})$ , we investigate counterparts of the classical Hardy-Littlewood and Riesz inequa…

math.AP2023

Mean-to-max ratio of the torsion function and honeycomb structures

Luca Briani, Dorin Bucur

In this paper we study extremal behaviors of the mean to max ratio of the $p$ -torsion function with respect to the geometry of the domain. For $p$ larger than the dimension of the…

math.AP2022

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 $S^{n} \subseteq R^{n + 1}$ is maximized by the union of tw…

math.AP2016

The quantitative Faber-Krahn inequality for the Robin Laplacian

D. Bucur, V. Ferone, C. Nitsch +1

We prove a quantitative Faber-Krahn inequality for the first eigenvalue of the Laplace operator with Robin boundary conditions. The asymmetry term involves the square power of the…

math.OC2014

A surgery result for the spectrum of the Dirichlet Laplacian

Dorin Bucur, Dario Mazzoleni

In this paper we give a method to geometrically modify an open set such that the first $k$ eigenvalues of the Dirichlet Laplacian and its perimeter are not increasing, its measure…