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Moser functions and fractional Moser-Trudinger type inequalities

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

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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 $\Omega$.
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

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