A priori gradient bounds for fully nonlinear parabolic equations and   applications to porous medium models
  We prove a priori gradient bounds for classical solutions of the fully nonlinear parabolic equation $$u_{t}=F(D^2u,D u,u,x,t).$$ The domain is the torus {\mathbb{T}}^{d} of dimension $d\ge1$. Up to the price of technicalities, our work can be extended to the case of bounded domains or the case of the whole space ${\mathbb{R}}^d$. Several applications are given, including the standard porous medium equation. 
Hana Hajj Chehade (LAMFA), Mustapha Jazar, R\'egis Monneau (CERMICS)
math.AP