A priori gradient bounds for fully nonlinear parabolic equations and applications to porous medium models

Hana Hajj Chehade, Mustapha Jazar, Régis Monneau

We prove a priori gradient bounds for classical solutions of the fully nonlinear parabolic equation $$u_t=F(D^{2}u,Du,u,x,t).$$ The domain is the torus {\mathbb{T}}^{d} of dimensi…