### Abstract

The goal of the work is to verify the fractional Leibniz rule for Dirichlet Laplacian in the exterior domain of a compact set. The key point is the proof of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet problem.

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

Pages (from-to) | 1101-1115 |

Number of pages | 15 |

Journal | Discrete and Continuous Dynamical Systems- Series A |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2019 Feb 1 |

### Fingerprint

### Keywords

- Dirichlet problem
- Exterior domains
- Fractional Leibniz rule
- Gradient estimates
- Heat equations

### ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete and Continuous Dynamical Systems- Series A*,

*39*(2), 1101-1115. https://doi.org/10.3934/dcds.2019046

**On fractional Leibniz rule for dirichlet laplacian in exterior domain.** / Gueorguiev, Vladimir Simeonov; Taniguchi, Koichi.

Research output: Contribution to journal › Article

*Discrete and Continuous Dynamical Systems- Series A*, vol. 39, no. 2, pp. 1101-1115. https://doi.org/10.3934/dcds.2019046

}

TY - JOUR

T1 - On fractional Leibniz rule for dirichlet laplacian in exterior domain

AU - Gueorguiev, Vladimir Simeonov

AU - Taniguchi, Koichi

PY - 2019/2/1

Y1 - 2019/2/1

N2 - The goal of the work is to verify the fractional Leibniz rule for Dirichlet Laplacian in the exterior domain of a compact set. The key point is the proof of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet problem.

AB - The goal of the work is to verify the fractional Leibniz rule for Dirichlet Laplacian in the exterior domain of a compact set. The key point is the proof of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet problem.

KW - Dirichlet problem

KW - Exterior domains

KW - Fractional Leibniz rule

KW - Gradient estimates

KW - Heat equations

UR - http://www.scopus.com/inward/record.url?scp=85056459794&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056459794&partnerID=8YFLogxK

U2 - 10.3934/dcds.2019046

DO - 10.3934/dcds.2019046

M3 - Article

VL - 39

SP - 1101

EP - 1115

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

SN - 1078-0947

IS - 2

ER -