Moser-Trudinger And Adams Type Inequalities And Their Applications
نویسندگان
چکیده
MOSER-TRUDINGER AND ADAMS TYPE INEQUALITIES AND THEIRAPPLICATIONSbyNGUYEN LAMAugust 2014Advisor: Dr. Guozhen LuMajor: MathematicsDegree: Doctor of PhilosophyIn this dissertation, we study some variants of the Moser-Trudinger inequalities and Adamsinequalities. The proofs of these inequalities relied crucially on the symmetrization arguments inthe literature. By proposing new arguments and approaches, we develop successfully the criticalversions of these well-known inequalities in many different settings where the rearrangementarguments may not be existed. As applications of our results, we also study in this dissertationthe elliptic equations that contain the exponential nonlinearities.
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