2.3k citations · 4k across the 36 of their papers we have counts for
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On the differentiability of the solution to an equation with drift and fractional diffusion
Luis Silvestre
We consider an equation with drift and either critical or supercritical fractional diffusion. Under a regularity assumption for the vector field that is marginally stronger than wh…
On Divergence-free Drifts
Gregory Seregin, Luis Silvestre, Vladimir Sverak +1
We investigate the validity and failure of Liouville theorems and Harnack inequalities for parabolic and elliptic operators with low regularity coefficients. We are particularly in…
Upper bounds for multiphase composites in any dimension
Luis Silvestre
We prove a rigorous upper bound for the effective conductivity of an isotropic composite made of several isotropic components in any dimension. This upper bound coincides with the…
Holder estimates for advection fractional-diffusion equations
Luis Silvestre
We analyse conditions for an evolution equation with a drift and fractional diffusion to have a Holder continuous solution. In case the diffusion is of order one or more, we obtain…
The Dirichlet problem for the convex envelope
Luis Silvestre, Adam M. Oberman
The Convex Envelope of a given function was recently characterized as the solution of a fully nonlinear Partial Differential Equation (PDE). In this article we study a modified pro…