Applications of Optimal Mass Transportation in Geometric and Functional Inequalities
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In this thesis, our aim is to first layout the framework of optimal transport, and then demonstrate its usefulness in proving functional inequalities. This approach is advantageous as it provides extremely efficient proofs, while requiring potentially less work than when using a classical approach. In particular, the optimal transport approach grants the ability to prove inequalities with sharp constants and pinpoints conditions for which they hold with equality. For example, in the case of the Gagliardo-Nirenberg-Sobolev (GNS) Inequality, optimal transport recovers the inequality for arbitrary norms in $\mathbb{R}^n$.
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Copyright © 2022 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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- 2022
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valentino-applicationsofoptimalmasstransportationin.pdf | 2023-05-05 | Public | Download |