Sharp certain Sobolev-type inequalities via optimal transport
碩士 === 國立臺灣大學 === 數學研究所 === 100 === In this thesis, we first give a proof of the Monge mass transport problem for the special quadratic cost function, and use the optimal map which we constructed to sharp certain Sobolev-type inequalities. We show that mass transportation methods provide an elementa...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Others |
| Language: | en_US |
| Published: |
2012
|
| Online Access: | http://ndltd.ncl.edu.tw/handle/16518467863158346399 |
| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 100 === In this thesis, we first give a proof of the Monge mass transport problem for the special quadratic cost function, and use the optimal map which we constructed to sharp certain Sobolev-type inequalities. We show that mass transportation methods provide an elementary approach to the study of certain Sobolev-type inequalities. The Euclidean structure of n-dimensional Euclidean space plays no role in our approach. Besides, to complete our work, we
mainly consult the paper [3] and [7].
|
|---|