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Local and nonlocal problems regarding the Q-curvature and the Adams-Moser-Trudinger inequalities

Hyder, Ali. Local and nonlocal problems regarding the Q-curvature and the Adams-Moser-Trudinger inequalities. 2017, Doctoral Thesis, University of Basel, Faculty of Science.

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Official URL: http://edoc.unibas.ch/diss/DissB_12192

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Abstract

We study the existence and classification of solutions to a Q-curvature problem in R^n with finite volume. Inspired by the previous works of Lin and Martinazzi in even dimension and Jin-Maalaoui-Martinazzi-Xiong in dimension three we classify all solutions in terms of their behavior at infinity. Extending the work of Wei-Ye we proved the existence of solution with prescribed volume and asymptotic behavior, under certain restrictions. In the case when the dimension n is bigger than four, we show that the volume of the conformal metric can be prescribed arbitrarily.
We also study a sharp Adams-Moser-Trudinger type inequality in a fractional settings. As an application, improving upon works of Adimurthi and Lakkis, we prove existence of solutions to a Moser-Trudinger equation.
Advisors:Martinazzi, Luca and Malchiodi, Andrea
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Analysis (Martinazzi)
UniBasel Contributors:Hyder, Ali and Martinazzi, Luca
Item Type:Thesis
Thesis Subtype:Doctoral Thesis
Thesis no:12192
Thesis status:Complete
Bibsysno:Link to catalogue
Number of Pages:1 Online-Ressource (v, 134 Seiten)
Language:English
Identification Number:
Last Modified:22 Jan 2018 15:52
Deposited On:17 Jul 2017 13:38

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