An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift
François Hamel, Nikolaï Nadirashvili, Emmanuel Russ · Comptes Rendus Mathématique · 2005
We generalize the classical Rayleigh–Faber–Krahn inequality to the case of the Dirichlet Laplacian with a drift. We also solve some optimization problems for the principal eigenvalue of the operator − Δ + v ⋅ ∇ in a fixed domain with a control of the drift v in L ∞ .