科研之友
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摘要
For f convex and increasing, we prove the inequality integral f(vertical bar U'vertical bar) >= integral f (nT'), every time that U is a Sobolev function of one variable and T is the non-decreasing map defined on the same interval with the same image measure as U, and the function n(x) takes into account the number of pre-images of U at each point. This may be applied to some variational problems in a mass-transport framework or under volume constraints.
- 出版日期2012-3
