Diffusion bounds for non-autonomous degenerate parabolic equations

Abstract

We consider possibly degenerate non-autonomous parabolic equations in $L^p$ spaces for all $1\le p\le \infty$, and prove Gaussian space-time upper bounds of the Davies-Gaffney, or integrated Nash-Aronson, type on their solutions. Our bounds cover both linear and nonlinear equations.

28pp, 2 figures. v1->v2: streamlined proof & statement of main results