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The heat flow as gradient flow on the space of probability measures

Francesco Nobili
Institution: 
SISSA
Location: 
A-136
Schedule: 
Friday, June 28, 2019 - 14:00
Abstract: 

The seminar aims at presenting the heat flow in the language of gradient flows for educational purposes. It is divided into two parts. Firstly, we show how to recover the problem of the heat flow as the gradient flow of the Cheeger energy. In this part, we briefly present the gradient flow theory in a Hilbert setting, and we show how to generalise it in a purely metric framework under certain compatibility assumptions in energy and distance. Finally, exploiting tools from Optimal Transport in the simpler Euclidean setting, we recover the heat flow as a gradient flow on the space of probability measures associated with a certain entropy functional. 

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