## Abstract

In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in the equilateral cylinder among all Euclidean triangular cylindric domains of a given volume as well as we obtain spectral geometric inequalities of the Cauchy-Dirichlet-Neumann heat operator in the right and equilateral triangular cylinder. It is also established that maximum of the second s-number of the Cauchy-Neumann heat operator is reached by the equilateral triangular cylinder among all triangular cylinders of given volume. In addition, we prove that the second s-number of the Cauchy-Neumann heat operator is maximized in the circular cylinder among all cylindrical Lipschitz domains of fixed volume.

Original language | English |
---|---|

Title of host publication | Functional Analysis in Interdisciplinary Applications |

Editors | Erlan D. Nursultanov, Tynysbek Sh. Kalmenov, Makhmud A. Sadybekov, Michael V. Ruzhansky |

Publisher | Springer New York |

Pages | 349-362 |

Number of pages | 14 |

Volume | 216 |

ISBN (Print) | 9783319670522 |

DOIs | |

Publication status | Published - Jan 1 2017 |

Externally published | Yes |

Event | International Conference on Functional analysis in interdisciplinary applications, FAIA 2017 - Astana, Kazakhstan Duration: Oct 2 2017 → Oct 5 2017 |

### Conference

Conference | International Conference on Functional analysis in interdisciplinary applications, FAIA 2017 |
---|---|

Country | Kazakhstan |

City | Astana |

Period | 10/2/17 → 10/5/17 |

## Keywords

- Heat operator
- Isoperimetric inequalities
- Non-selfadjoint operator
- Polya inequality
- S-Number

## ASJC Scopus subject areas

- Mathematics(all)