Hyder, Ali.
(2015)
* Moser functions and fractional Moser-Trudinger type inequalities.*
Preprints Fachbereich Mathematik, 2015 (32).

PDF
- Published Version
825Kb |

Official URL: https://edoc.unibas.ch/69995/

Downloads: Statistics Overview

## Abstract

We improve the sharpness of some fractional Moser-Trudinger type inequalities, particularly those studied by Lam-Lu and Martinazzi. As an application, improving upon works of Adimurthi and Lakkis, we prove the existence of weak solutions to the problem

\[

(−∆)^{n/2} u = \lambda u e^{bu^2} in \Omega, 0 < \lambda < \lambda_1, b > 0,

\]

with Dirichlet boundary condition, for any domain $\Omega$ in $\mathbb{R}$ with finite measure. Here $\lambda_1$ is the first eigenvalue of $(−∆)^{n/2}$ on $\Omega$.

\[

(−∆)^{n/2} u = \lambda u e^{bu^2} in \Omega, 0 < \lambda < \lambda_1, b > 0,

\]

with Dirichlet boundary condition, for any domain $\Omega$ in $\mathbb{R}$ with finite measure. Here $\lambda_1$ is the first eigenvalue of $(−∆)^{n/2}$ on $\Omega$.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Analysis (Martinazzi) 12 Special Collections > Preprints Fachbereich Mathematik |
---|---|

UniBasel Contributors: | Hyder, Ali |

Item Type: | Preprint |

Publisher: | Universität Basel |

Language: | English |

Last Modified: | 09 May 2019 09:01 |

Deposited On: | 28 Mar 2019 09:51 |

Repository Staff Only: item control page