現代数学の系譜工学物理雑談古典ガロア理論も読む78

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545: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/11/06(水) 00:33:52.86 ID:i9ghHS7z

>>544

”Monge-Ampere Differential Equation
The solutions are given by a system of differential equations given by Iyanaga and Kawada (1980).”か
https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2018/Figalli-Citation.pdf
? Figalli short citation ?
For contributions to the theory of optimal transport and its applications in
partial differential equations, metric geometry and probability.

? Figalli long citation ?
Alessio Figalli has made multiple fundamental advances in the theory of
optimal transport, while also applying this theory in novel ways to other
areas of mathematics. Only a few of his numerous results in these areas are
described here.
Figalli’s joint work with De Philippis on regularity for the Monge-Amp`ere
equation is a groundbreaking result filling the gap between gradient estimates
discovered by Caffarelli and full Sobolev regularity of the second derivatives
of the convex solution of the Monge-Amp`ere equation with merely bounded
right-hand side. The result is almost optimal in view of existing counterexamples. It has direct implications on regularity of the optimal transport
maps, and on regularity to semigeostrophic equations.
Figalli initiated the study of the singular set of optimal transport maps and
obtained the first definite results in this direction: he showed that it has
null Lebesgue measure in full generality. He has also given significant contributions to the theory of obstacles problems, introducing new methods to
analyze the structure of the free boundary.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1571400076/545

546: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [] 2019/11/06(水) 00:34:16.71 ID:i9ghHS7z

>>545
つづき

Figalli and his coauthors have also applied optimal transport methods in
a striking fashion to obtain sharp quantitative stability results for several
fundamental geometric inequalities, such as the isoperimetric and BrunnMinkowski inequalities, without any additional assumptions of regularity on
the objects to which these inequalities are applied; the methods are also
not reliant on Euclidean symmetries, extending in particular to the Wulff
inequality to yield a quantitative description of the low-energy states of crystals.

https://en.wikipedia.org/wiki/Monge%E2%80%93Amp%C3%A8re_equation
Monge?Ampere equation

Monge?Ampere equations frequently arise in differential geometry, for example, in the Weyl and Minkowski problems in differential geometry of surfaces. They were first studied by Gaspard Monge in 1784[1] and later by Andre-Marie Ampere in 1820[2].

http://mathworld.wolfram.com/Monge-AmpereDifferentialEquation.html
Wolfram Research, Inc.
Monge-Ampere Differential Equation
The solutions are given by a system of differential equations given by Iyanaga and Kawada (1980).
Iyanaga, S. and Kawada, Y. (Eds.). "Monge-Ampere Equations." §276 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 879-880, 1980.

https://ja.wikipedia.org/wiki/%E5%BD%8C%E6%B0%B8%E6%98%8C%E5%90%89
彌永 昌吉（いやなが しょうきち、1906年4月2日 - 2006年6月1日）
https://en.wikipedia.org/wiki/Shokichi_Iyanaga
Shokichi Iyanaga (彌永 昌吉 Iyanaga Sh?kichi, April 2, 1906 ? June 1, 2006)
以上

http://rio2016.5ch.net/test/read.cgi/math/1571400076/546

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