A partial Laplacian on a quotient Hilbert space and on the Wasserstein space

Wilfrid Gangbo (UCLA)

Friday, January 17, 2020 -
12:00pm to 1:00pm
Location:
Physics 130

We consider the quotient of the Hilbert space $L^2((0,1)^d;\mathbb{R}^d)= \mathbb{R}^d\oplus\mathbb{H}_0$, by the set of measure preserving maps on $(0, 1)^d$. This is nothing but the set of Borel measures of finite second moments on $\mathbb{R}^d$. We study a partial trace of the hessian on a subset of functions defined on the quotient space and verify a distinctive smoothing effect of the "heat flows" they generate for a particular class of initial conditions. To this end, we develop a theory of Fourier analysis and conic surfaces and identify a measure which allows for an integration by parts. (This is a joint work with Y.T. Chow).

Last updated: 2020/05/29 - 2:41pm