Vincent Boulard

collaborators

4 papers

math.AP2026

Generic failure of uniform separation in planar Dirichlet spectra

Vincent Boulard

Can a bounded planar domain have a simple Dirichlet spectrum with uniformly separated consecutive eigenvalues? Dimension two is critical: Weyl's law permits both uniform separation…

math.AP2026

Optimal geometric barriers for weighted observability of heat semigroups on metric measure spaces

Vincent Boulard, Amaury Hayat, Emmanuel Trélat

Weighted integrated observability inequalities for heat equations usually involve a small-time factor of the form $e^{- γ / t}$ . We prove that this scale is not an artefact of Carlema…

math.AP2026

Generic non-vanishing of Dirichlet eigenfunction averages and absence of symmetries

Vincent Boulard

We prove that, for a generic $C^{m}$ -domain $Ω \subset R^{d}$ (with $m \geq 3$ , $d \geq 2$ ) in the sense of Baire category for the Micheletti topology, every Dirichlet-Laplacian…

math.AP2025

F-equivalence for parabolic systems and applications to the stabilization of nonlinear PDE

Vincent Boulard, Amaury Hayat

We consider the $F$ -equivalence problem for parabolic systems: under which conditions a control system, governed by a parabolic operator $A$ and a control operator $B$ , can be made…