Sharp certain Sobolev-type inequalities via optimal transport
Date Issued
2012
Date
2012
Author(s)
Hsu, Wei-Ming
Abstract
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].
Subjects
optimal transport
Monge mass transport problem
sharp constants
Sobolev inequality
Gagliardo-Nirenberg inequality
Type
thesis
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