175 citations · 729 across the 112 of their papers we have counts for
8 papers · 2 filters
Potential theory for nonlocal drift-diffusion equations
Quoc-Hung Nguyen, Simon Nowak, Yannick Sire +1
The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion equations via pointwise potential estimates. Our analysis requires only minimal assum…
Finite-time singularity formation for the heat flow of the -system
Yannick Sire, Juncheng Wei, Youquan Zheng +1
We construct the first example of finite time blow-up solutions for the heat flow of the -system, describing the evolution of surfaces with constant mean curvature \begin{equati…
Nonlocal degenerate Isaacs operators: Hölder regularity
Isabeau Birindelli, Giulio Galise, Yannick Sire
We show that bounded viscosity solutions of some nonlocal degenerate Isaacs type operators of order are Hölder continuous, provided is sufficiently close to 1. As an appli…
Global Existence of Weak Solutions to the Two Dimensional Nematic Liquid Crystal Flow with Partially Free Boundary
Yannick Sire, Yantao Wu, Yifu Zhou
We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in . We prove regularity estimates and the global existence of weak…
Gradient regularity for fully nonlinear equations with degenerate coefficients
David Jesus, Yannick Sire
We derive estimates for viscosity solutions of fully nonlinear equations degenerating on a hypersurface.
On the heat kernel of the Rumin complex and Calderón reproducing formula
Paolo Ciatti, Bruno Franchi, Yannick Sire
We derive several properties of the heat equation with the Hodge operator associated with the Rumin complex on Heisenberg groups and prove several properties of the fundamental sol…