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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
2
votes
Elliptic Regularity with Gibbs Measure Satisfying Bakry-Emery Condition
For the estimate of the Hessian you might use Bochner's formula: on such weighted $R^d$ for any smooth compactly supported function $u$ it holds
$$
\nabla^*\nabla\frac{|\nabla u|^2}2=|D^2u|^2+\langle\ …
2
votes
Heat kernel and convergence
As said, this holds if the manifolds have Ricci curvature uniformly bounded from below. Perhaps the quickest reference for this convergence is my paper
https://link.springer.com/article/10.1007/s0052 …
8
votes
Accepted
Reference request: Wasserstein metric spaces for non linear weights/mobility?
Yes, this issue has been considered. You can start having a look at `A new class of transport distances between measures' by Dolbeault, Nazaret and Savaré (http://link.springer.com/article/10.1007%2F …
0
votes
Regular Lagrangian flow for explicit ODE with discontinuous right-hand side
No. The theory of Regular Lagrangian Flows rests on two key assumptions: a Sobolev/BV regularity of the vector field and a bound from below on its divergence.
In your case you are solving
$$
X'=b(X)
$ …