Isoperimetric Inequalities for the Heat Potential Operator

Tynysbek Sh. Kal'menov, Aidyn Kassymov, Durvudkhan Suragan


In this paper we prove that the circular cylinder is a maximizer of the
Schatten $p$-norm of heat potential operator among all Euclidean cylindric
domains of a given measure. We also give analogues of a Rayleigh-Faber-Krahn and a Hong-Krahn-Szeg\"{o} type inequalities.

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