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...

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Bibliographic Details
Main Authors:	Wei-Ming Hsu, 許為明
Other Authors:	Ai-Nung Wang
Format:	Others
Language:	en_US
Published:	2012
Online Access:	http://ndltd.ncl.edu.tw/handle/16518467863158346399

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spelling	ndltd-TW-100NTU054790302015-10-13T21:50:18Z http://ndltd.ncl.edu.tw/handle/16518467863158346399 Sharp certain Sobolev-type inequalities via optimal transport 以最優運輸方法確定某些索伯列夫型不等式中的最佳常數 Wei-Ming Hsu 許為明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]. Ai-Nung Wang 王藹農 2012 學位論文 ; thesis 81 en_US
collection	NDLTD
language	en_US
format	Others
sources	NDLTD
description	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].
author2	Ai-Nung Wang
author_facet	Ai-Nung Wang Wei-Ming Hsu 許為明
author	Wei-Ming Hsu 許為明
spellingShingle	Wei-Ming Hsu 許為明 Sharp certain Sobolev-type inequalities via optimal transport
author_sort	Wei-Ming Hsu
title	Sharp certain Sobolev-type inequalities via optimal transport
title_short	Sharp certain Sobolev-type inequalities via optimal transport
title_full	Sharp certain Sobolev-type inequalities via optimal transport
title_fullStr	Sharp certain Sobolev-type inequalities via optimal transport
title_full_unstemmed	Sharp certain Sobolev-type inequalities via optimal transport
title_sort	sharp certain sobolev-type inequalities via optimal transport
publishDate	2012
url	http://ndltd.ncl.edu.tw/handle/16518467863158346399
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Sharp certain Sobolev-type inequalities via optimal transport

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