In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in a circular cylinder among all Euclidean cylindric domains of a given measure. It is an analogue of the Rayleigh-Faber-Krahn inequality for the heat operator. We also prove a Hong-Krahn-Szegö and a Payne-Pólya-Weinberger type inequalities for the Cauchy-Dirichlet heat operator.
- Cauchy-Dirichlet heat operator
- Hong-Krahn-Szegö inequality
- Payne-Pólya-weinberger inequality
- Rayleigh-Faber-Krahn inequality
ASJC Scopus subject areas