Diffusion bounds for non-autonomous degenerate parabolic equations

TL;DR

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Contribution

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Abstract

We prove the Davies-Gaffney (i.e., integrated Nash-Aronson) type diffusive upper bounds on the propagators of parabolic equations in $L^p$-sense for all $1\le p\le\infty$. Our approach is based on a simple exponential deformation argument that does not require hypoellipticity. It provides a unified approach to diffusive upper bounds that covers a wide class of problems including degenerate, non-autonomous, and non-linear equations.