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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\ …
Nicola Gigli's user avatar
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 …
Nicola Gigli's user avatar
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 …
Nicola Gigli's user avatar
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) $ …
Nicola Gigli's user avatar