Some stability results for perturbed semilinear parabolic equations (Q1198691)

A famous result by Brascamp-Lieb says that in a bounded strongly convex domain, the principal eigenfunction of \(-\Delta\), subject to Dirichlet boundary conditions, is log-concave. In this paper the authors prove the same result for a periodic-parabolic eigenvalue problem. This result does not immediately follow from the known concavity results since it is always assumed there that one starts with a log-concave initial condition (whereas this is one of the unknowns in periodic problems).