An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift

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 $?\mathrm{\Delta }+v?\mathrm{?}$ in a fixed domain with a control of the drift v in $L^{\infty }$. To cite this article: F. Hamel et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).