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arXiv · 2603.19540

Diffusion bounds for non-autonomous degenerate parabolic equations

Marius Lemm·Israel Michael Sigal·Jingxuan Zhang
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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.

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Marius Lemm, Israel Michael Sigal, Jingxuan Zhang. 2026-03-20. Diffusion bounds for non-autonomous degenerate parabolic equations. https://arxiv.org/abs/2603.19540

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