Moser-Nash kernel estimates for degenerate parabolic equations (Q509733)

The paper deals with fundamental solutions of a class of degenerate parabolic equations of the form \[ u_t-\text{div }{\mathbf A}(t,x,u,Du)=0 \qquad \text{on}\;{\mathbb R}^N \times (0,\infty) \] of ``\(p\)-Laplacian type'' with \(p>2\). Optimal estimates for fundamental solutions as well as the existence of such solutions are established by the DiBenedetto-De Giorgi approach. The main challenge with respect to earlier work is the finite propagation speed. The results for the \(p\)-Laplacian carry over to porous media and Fokker-Plank equations.