基于Nash–Moser迭代的黎曼流形上过滤方程的微分Harnack估计
Differential Harnack Estimates and Frequency Monotonicity for Filtration Equations on Riemannian Manifolds
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中文总结 AI 辅助
该研究针对黎曼流形上过滤方程的光滑正解，通过Bochner判别式结合Nash–Moser迭代推导微分Harnack估计，恢复了两类方程的经典估计并拓展了过滤律类型。
中文摘要 AI 辅助
我们在完备黎曼流形上的一致抛物范围内，对过滤方程 $u_t=\Delta F(u)$ 的光滑正解证明了局部微分Harnack估计。Bochner判别式论证得到一个强制的正部不等式，该不等式通过Nash–Moser迭代闭合。我们推导了Harnack和Liouville结果，恢复了多孔介质方程和快速扩散方程的Aronson-Bénilan估计，并描述了一类真正非幂次的过滤律。
英文摘要
In this work we derive local differential Harnack estimates for positive solutions of filtration equations on complete Riemannian manifolds with a lower Ricci curvature bound by using Nash--Moser iteration. Inspired by earlier work on parabolic frequency functions, we establish some new frequency monotonicity formulas for these equations. The results cover the porous-medium and fast-diffusion equations, as well as several non-power diffusion laws.
