2.3k citations · 4k across the 36 of their papers we have counts for
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Propagation in a non local reaction diffusion equation with spatial and genetic trait structure
Henri Berestycki, Tianling Jin, Luis Silvestre
We study existence and uniqueness of travelling fronts, and asymptotic speed of propagation for a non local reaction diffusion equation with spatial and genetic trait structure.
Regularity for parabolic integro-differential equations with very irregular kernels
Russell W. Schwab, Luis Silvestre
We prove Hölder regularity for a general class of parabolic integro-differential equations, which (strictly) includes many previous results. We present a proof which avoids the use…
A new regularization mechanism for the Boltzmann equation without cut-off
Luis Silvestre
We apply recent results on regularity for general integro-differential equations to derive a priori estimates in Hölder spaces for the space homogeneous Boltzmann equation in the n…
A non local Monge-Ampere equation
Luis Caffarelli, Luis Silvestre
We introduce a non local analog to the Monge-Ampere operator and show some of its properties. We prove that a global problem involving this operator has C 1,1 solutions in the full…
On a transport equation with nonlocal drift
Luis Silvestre, Vlad Vicol
In \cite{CordobaCordobaFontelos05}, Córdoba, Córdoba, and Fontelos proved that for some initial data, the following nonlocal-drift variant of the 1D Burgers equation does not have…
On Landis' conjecture in the plane
Carlos Kenig, Luis Silvestre, Jenn-Nan Wang
In this paper we prove a quantitative form of Landis' conjecture in the plane. Precisely, let be a measurable real vector-valued function and be a real measurabl…