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Results tagged with calculus-of-variations
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user 106046
Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
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Optimal transport for applied mathematicians: how does $\varphi (x) = \inf_{y \in Y} [c(x, y...
I hope I did not misunderstand the question, but it seems $\varphi(x) > - \infty$ holds as follows if $(x, y) \in \Gamma$:
For any $(x_i, y_i) \in \Gamma$, $i=1, \dots, n$, we see that
\begin{align}
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