Luis Silvestre
Core Contributions
Silvestre is a central figure in the field of nonlocal partial differential equations. He collaborated with Caffarelli to establish the regularity theory framework for the fractional Laplacian, and has made breakthrough contributions in directions including nonlocal Navier-Stokes equations and fractional Monge-Ampere equations.
Selected Works
| Year | Work / Article | Problem Addressed |
|---|---|---|
| 2007 | "An extension problem related to the fractional Laplacian" (with Caffarelli) | Jointly established with Caffarelli the extension representation of the fractional Laplacian, converting nonlocal operators into higher-dimensional local degenerate elliptic operators |
| 2010 | "Hölder estimates for solutions of integro-differential equations like the fractional Laplace" | Independently established Holder regularity estimates for nonlocal integro-differential equations, proving interior regularity of solutions under general kernel conditions |
| 2012 | "On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion" | Solved the differentiability problem for solutions to the Hamilton-Jacobi equation with critical fractional diffusion, advancing the viscosity solution theory for nonlocal equations |