Open Access Dissertation
Date of Award
In this dissertation, we study some variants of the Moser-Trudinger inequalities and Adams inequalities. The proofs of these inequalities relied crucially on the symmetrization arguments in the literature. By proposing new arguments and approaches, we develop successfully the critical versions of these well-known inequalities in many different settings where the rearrangement arguments may not be existed. As applications of our results, we also study in this dissertation the elliptic equations that contain the exponential nonlinearities.
Lam, Nguyen, "Moser-Trudinger And Adams Type Inequalities And Their Applications" (2014). Wayne State University Dissertations. 1016.