Laboratoire d’Analyse et de Mathématiques Appliquées

Polygonal Faber-Krahn inequality: local minimality via validated computing

The main result of the paper shows that the regular [Formula: see text]-gon is a local minimizer for the first Dirichlet-Laplace eigenvalue among [Formula: see text]-gons having fixed area for [Formula: see text]. The eigenvalue is seen as a function of the coordinates of the ver...

A New Characterization of the Wulff Shape

We prove a new charcaterization of the Wulff shape in termes of higher order anisotropic mean curvatures. Namely, if a closed, connnected and oriented hypersurface of the Euclidean space has a constant higher order anisotropic mean curvature H F r and another one H F s almost con...

Optimal Vaccination Strategies for a Heterogeneous SIS Model

Abstract. We study in a general mathematical framework the optimal allocation of vaccine in an heterogeneous population. We cast the problem of optimal vaccination as a biobjective minimization problem [Formula: see text], where [Formula: see text] and [Formula: see text] stand,...

Global Boundedness Induced by Asymptotically Non‐Degenerate Motility in a Fully Parabolic Chemotaxis Model with Local Sensing

ABSTRACT A fully parabolic chemotaxis model of Keller–Segel type with local sensing is considered. The system features a signal‐dependent asymptotically non‐degenerate motility function, which accounts for a repulsion‐dominated chemotaxis. Global boundedness of classical solution...

The One-Dimensional Compressible Navier–Stokes Equations in Critical Regularity Spaces

Abstract. We are concerned with the barotropic compressible Navier–Stokes equations on the real line. Our primary goal is to establish the global well-posedness in a critical regularity framework in the case where the initial data are small perturbations of a stable constant stat...