An isoperimetric inequality for the principal eigenvalue of a periodic-parabolic problem (Q1093814)

The analogous of the Rayleigh-Faber-Krahn or the Szegö-Weinberger inequalities is derived for the principal eigenvalue related to a periodic-parabolic equation. The proof differs from the one for the elliptic case, based on the variational characterization of the eigenvalues. Nevertheless it makes use of standard inequalities for rearrangements. The author also discusses the case of equality and provides a counterexample for some statement by the reviewer [``Isoperimetric inequalities and applications'' (1980; Zbl 0436.35063)].