From the 3 of 4 linked papers with an AI index.
4 papers
Generic failure of uniform separation in planar Dirichlet spectra
Vincent Boulard
The paper proves that for bounded planar domains, having uniformly separated Dirichlet eigenvalues is non‑generic: in a natural Baire space of rough domains, the typical domain has…
Optimal geometric barriers for weighted observability of heat semigroups on metric measure spaces
Vincent Boulard, Amaury Hayat, Emmanuel Trélat
The paper proves that the exponential small‑time factor e^{-γ/t} in weighted observability inequalities for heat equations is dictated by the geometry of the observation set, estab…
Generic non-vanishing of Dirichlet eigenfunction averages and absence of symmetries
Vincent Boulard
The paper proves that for a generic smooth domain in Euclidean space, every Dirichlet Laplacian eigenfunction has a nonzero average, and shows that such generic domains have trivia…
F-equivalence for parabolic systems and applications to the stabilization of nonlinear PDE
Vincent Boulard, Amaury Hayat
We consider the -equivalence problem for parabolic systems: under which conditions a control system, governed by a parabolic operator and a control operator , can be made…